I don't think it would. No one felt the British army was some invincible force that was the only thing able to stand against Napoleon, so it losing (probably not for the first time, though I'd want to check Moore's retreat to be sure) would not be a dreadful shock.
It isn't the British army itself that's held in high regard but Wellington himself. He was seen as their best general, sent to the nearest theatre to France where he would have to absorb Napoleon's first blows while the rest of the Coalition pulled their armies together. Yet even he was surprised by the speed of the French advance. If Napoleon wins at Waterloo he would have finished off Allied Europe's shining general in a campaign of barely four days - definitely very deflating for the Allies.
France raising more troops doesn't mean that the Allies won't be, and the issue of horses for the cavalry and artillery is not something there's a quick or easy solution for - which makes his position much weaker than in his prime.
OTL, the lack of cavalry at Bautzen and Lutzen meant Napoleon could not pursue the enemy his infantry had already defeated. A lack of horses would weaken his position, sure, but not fatally so, especially fighting on home ground. And Napoleon seemed to have more than enough artillery at Waterloo, in fact, a hundred more guns than Wellington did.
Surely the true comparison is the campaign of 1814.
In that, Iirc, Napoleon didn't win just one victory, but several, some of them impressive. But with what result? The Allies just picked themselves up, replaced their losses, and pressed on to Paris. Is there any reason to expect a different outcome the following year?
The difference is that Napoleon actually has more men at hand in 1815 than he did a year earlier. In the Six Days' Campaign he fought with barely 30,000 against 120,000 enemy troops, and that number ballooned to half a million
already in the theatre. In 1815 he has 120,000 with him to march into Belgium, at least 66,000 more recruits waiting in the depots, 10-20,000 men including Guard detachments in the Vendeé quelling a revolt that will soon be over, and the admittedly miniscule detachments protecting the rest of France's borders. Nevertheless, if he won at Waterloo, Napoleon would soon have had a field army to nearly equal the force he had in 1805. The Allies may be stronger now, more united, but surely we can't completely dismiss his chances in this campaign?
In a best case scenario, this is what I see happens. After defeating or driving away the British army at Waterloo, he pays great care to maintain the illusion that the army remains in Belgium, when in fact Napoleon is moving south to meet the Austrian army of Scwarzenberg, still separated by some distance into two 100,000-strong bulks.
When the Austrian right wing (composed mostly of Bavarian troops under Prince Wrede) gets news of Waterloo he halts (as in OTL) at Nancy to wait for the Russian army to arrive - it should be mustered at Kaiserslautern by July 1. Wrede's last encounter with Napoleon was an attempt to block the French retreat from Leipzig in which he managed to lose 9,000 troops. By the time he realises Napoleon's field force is coming for him, it is too late to withdraw safely over the Saar, and the Rhine presents no secure path of retreat as General Rapp still holds Strasbourg (also as in OTL). Scwarzenberg will attempt to send the left wing up north from the Swiss border as quickly as possible but there is little time before the French army reaches the now-outnumbered Austrian right wing. On French soil, surely Napoleon can wage the battle he likes best, cutting the Austrians off from retreat via Saarbrucken, fighting a quick action and forcing the surrender of the bulk of their forces.
The Austrian left wing will attempt to flee back over the Rhine (which they should manage before Napoleon can catch them). The Russians will hesitate by necessity on the French border while the Allies regroup. They will hope to be joined by the remaining undefeated corps (such as Bulow's) of the Prussian army and Schwarzenberg's so-called left column - 100,000 strong. There will definitely be jitters after three such major defeats - Ligny, Waterloo, and perhaps the Battle of Metz. But (as in OTL) the Allies underestimated Napoleon's true strength of numbers. He will be joined by the 25,000 Frenchmen centered at Strasbourg under Rapp and attempt to strike the Russians arrayed along the Saar before they can be reinforced and commence the invasion.
It would be roughly 140,000 French troops against at most 200,000 Russian soldiers under de Tolly. Those are most definitely odds Napoleon can deal with. If he can defeat this force too the Allies must now surely at least consider peace with him, especially if he agrees to the 1792 borders.
It seems like a fantasy, maybe, but so do many episodes from Napoleon's story. The main difference from 1814 here is that the war will be following Napoleon's script from the start. The commencement of hostilities in 1815 came with more surprise to the Allies than any of Napoleon's previous wars. This showed itself in the Waterloo Campaign. Blucher and Wellington explicitly trusted each other, so much so that they were described as the war's Malborough and Eugene - but even they let their armies separate, failing to anticipate the boldness and rapidity of the French offensive that nearly succeeded in completely separating the Allied force in half. All that in the space of four days. That Napoleon could do the same to other less competent commanders is a given.