Not likely. Castro's survived more assassination attempts than perhaps anyone, >300. Cuba is not East Germany. Castro came to power without USSR aid and survived its fall by several decades so far. If they could survive the loss of the USSR's subsidies in the late 80s/early 90s, they could do the same earlier.
If anything, you might see Castro turning to tourism as a solution even sooner. Since the country has slightly liberalized in the past few years, and likely will even more in the future, you might conceivably see an even more open Cuba by today. Likely Nixon and Kissinger are smart enough to recognize that and exploit an opening to split Cuba away from the USSR, much like their opening up to China.