Interesting thought......but I agree with the fact Napoleon's position was practically untenable from the outset and any intention to continue the war after a defeat or even a victory would just delay the inevitable. Napoleon began the Waterloo Campaign with the hope and idea of a 'decisive blow' against the allies shaking their resolve to continue the war. However, even if Napoleon had won the Battle of Waterloo, the best he could have hoped for, in my opinion, would be a chance to sue for peace from a relative position of strength. A victory over the great hero of the Peninsula, Wellington, and Prince Blucher , may have, in theory, induced the Austrians and Russians, massing on France's eastern border to reassess the situation, and maybe come to the negotiating table along with the rest of the allies, as the allied campaign lost momentum after such a disastrous defeat. But this was a long shot to say the very least.
Could Napoleon have fought on after the defeat at Waterloo? In my opinion perhaps, but again it would have been delaying the inevitable. The French retreat was surprisingly quite orderly, considering the disarray on the battlefield and remained so for several days. As far as I understand, no French Eagle was lost during the retreat. Eye-witness accounts say that by the time the French Army reached Paris, they were in good battle order; and Grouchy’s 30,000 men were almost unscathed during the retreat. So, as a military unit they perhaps could have fought on. However, Napoleon's state of mind has to be called into account. Napoleon as a military commander was past his best by 1815. The indecisiveness evident at Waterloo that has been well documented in historical accounts would, perhaps continue and would affect the performance of his army during any subsequent campaign. A good book that illustrates the state of mind of Napoleon is David Markham's 'The Road to Saint Helena: Napoleon after Waterloo'.
Politically, equally it would be difficult for Napoleon to fight on. Napoleon took a massive gamble in seizing power in 1815; however he had a good measure of popular support across France. However, some areas, notably rural areas didn't offer much support, Normandy, Brittany and Provence were cool towards Napoleon and the Royalist Vendee were in insurrection, which tied down around 6,000 French troops. While many French people remained loyal to Napoleon Bonaparte by nature, to ask them to support a war on all fronts after a defeat, as France, additionally was threatened with invasion, so soon after 1814 would be asking a lot. In addition, there were some of influence who conspired against him during this period, most notably Joseph Fouche who 'feathered his own nest' at the expense of Napoleon. Talleyrand was in negotiation with the Allies before Napoleon's 1814 abdication. On the other hand, many remained loyal (the majority of his Marshals) and fought alongside him and this may have been crucial if the war continued.
However, while he did have Ney, although rash with the use of the French cavalry at Waterloo, was still a very capable commander, Davout defending Paris, D'Erlon commanding the I Corps of the Armee du Nord and Suchet in Italy, to continue the war it would take massive organisational skills on behalf of Napoleon to organise the remaining troops in France (a sizeable amount it must be said) into a coherent fighting force ready to face the onslaught ahead of them. Napoleon, increasingly ill, indecisive and defeated in an epic battle where his tactics failed, may not have been up to the task. Also, the sound of 'La Garde Recule!' from Mont St Jean as they faced the British muskets would have been a massive psychological blow not just to him, but to the French army as a whole.
However, we must not forget the zeal in which some prosecuted the war against Napoleon. The Allies declared war against Napoleon, not against France.....thus making him effectively an outlaw. The Prussians were amongst the most zealous of Napoleon's enemies at this time. They were almost on a crusade of vengeance, a 'War of Liberation' in reply to the humiliation Napoleonic France had put Prussia through since 1806.A good insight into the determination of the Prussians to finally destroy the threat of Napoleon is in Michael Mann's book '...and they Rode On', although a diary of a British cavalry Regiment during the campaign, points to the desire for vengeance amongst the Prussians. During the campaign the Prussians were a determined foe as their recovery after Ligny illustrates and I could not see them allowing Napoleon to take the initiative if the campaign continued into July, or even making peace with a Napoleon definitely on the backfoot. Faced with such determination, the Napoleon of 1815 would have found it difficult to prosecute the war effectively. Furthermore, after Leipzig in 1813, Napoleon was definitely 'on the run' and with the Austrians and Russians massing on France's borders, any attempt to continue the war after a defeat, would have just resulted in an even bigger battle a few weeks down the line with the pursuing Anglo-Dutch and Prussians as well as the Austrians and the Russians. It'd be Leipzig all over again.