The simple fact is that very little would have probably changed; when German troops marched into Prague on 15 March 1939 he was simply making de jure that which was already de facto: that Czechoslovakian independence had ended with the signing of the Munich Agreement.
The Munich agreement was signed on 30 September 1938 and, as per the agreement, German forces began occupying the so called ‘Sudetenland’ in stages from 1 October onwards. Under the agreement, those territories ‘of preponderantly German character’ were to be ceded to the Reich; the Czechs and French interpreted this as meaning territories with German majorities of 75 to 80%, however the German and British representatives insisted that a simple majority was all that was required for the territory to become German. Moreover, Czechs who had taken up residence in the region between 1918 and 1938 were not to be counted. Consequently, the Czechs lost even more land than was expected by them or the French. It needs to be remembered that Munich was a conference without Czech participation; the agreement was made between Britain, France and Germany, and presented to the Czechs as a fate accompli, as though Czechoslovakia were an Anglo-French colony rather than an independent and sovereign state. The reality was that Czech sovereignty ended the moment that the Chamberlain flew to see Hitler at Birchesgarten.
After Hitler had occupied all of the territory that he wanted in October 1938, occupation of the rest was simply unnecessary; Germany held Czechoslovakia’s throat in its jaws, the slightest pressure would crush the windpipe. The government of Edvard Beneš fell on October 5th, before the land transfer had even been completed. It was replaced by a new regime lead by Emil Hácha that was conservative, authoritarian and completely subservient to Berlin; in December 1938 the Communist Party was dissolved and all Jewish teachers in Czechoslovakia (or Czech-Slovakia as it was by this time) lost their jobs. In January 1939, the Czechs were instructed to withdraw from the League of Nations, join the Anti-Comintern Pact, accept German direction of its foreign policy, sign a preferential trade agreement with Germany and introduce the Nuremburg Race Laws in full (the dismissal of Jewish teachers in December had occurred without prompting from Berlin). The Germans also demanded and received millions of Francs worth of gold bullion from the Czech central bank. Clearly what remained of Czechoslovakia was a German colony even before the Wehrmacht paraded through Prague in March 1939.
Internationally little would have changed; the good feelings towards Germany generated by Munich in Britain and France were destroyed by Kristallnacht; the anti-Jewish pogrom of 9-10 November 1938. That revealed true nature of the Nazi regime to people internationally who had been largely indifferent or ignorant. When Goebbels’ propaganda machine started laying the groundwork for the invasion of Poland, no-one had any illusions as to what was actually going on; the British embassy in Berlin informed London that the exact same stories of abuses of ethnic Germans in Czechoslovakia that were published in the German newspapers prior to Munich were now being reprinted word for word, with only the town names changed from Czech to Polish. (Proof of just how short the time between the two events was and how little prior planning was actually involved; there simply wasn’t time to fabricate stories of new atrocities, so the old ones were recycled.) No-one in London, Paris, and particularly Warsaw would have been under any illusions that ceding Danzig and the Pomeranian Corridor to Hitler would have permitted Poland to keep any independence; it would have become every bit the puppet that Prague had become.
Assuming the same guarantees, diplomatic manoeuvres, and ultimate outbreak of war, the Polish campaign would have been largely unaffected; although some German forces did attack Poland from Slovakian territory, they were limited by the terrain and restricted roads, the bulk of the German army attacked directly out of Germany proper.
March 15 gave Hitler a parade and a night in Hradschin castle, little else.