As far as I know Colombus expected to be able to circumnavigate the world and reach Asia because he (mistakenly) thought the globe was much smaller than most people (correctly) thought.
If America hadn't been there, therefore, he would have failed on his mission of reaching Asia's on its Eastern coast. But would he just have gone on until they had run out of food and water, or were they planning on coming back if they hadn't found Asia within a certain amount of time?
If they didn't, were the other captains and the crew aware of the risk involved on betting that the Earth was small enough to reach land before dying?
A similar question - whether or not Columbus could have reached Asia if America wasn't there - was asked about a week and half ago, and my answer was "No":
This also has a longish discussion about Columbus's supplies, with u/terminus-trantor
However, this is only half of your question. The other half, would he have turned back, can in part be answered from Columbus's journal of his voyage. Columbus didn't believe he was sailing into a complete unknown - he expected land to be there, and was fairly confident of its approximate location. The important events related to this on the voyage to America were:
6th September: leaves the Canary Islands, towards America.
25th September: reaches the point where he expected some of the eastern islands of Asia. After discussion with the captain of the Pinta, they concluded that they might have missed them, or might not have quite reached them yet. They continued to the west.
3rd October: Columbus was convinced that they had sailed past the expected islands, and decided to continue to the west, to reach the Asian mainland rather than trying to find the islands.
10th October: "Here the people could endure no longer. They complained of the length of the voyage." Columbus was past where he had expected land, and his captains and crew showed signs that they might not go much further. Fernández de Oviedo's History of the Indies, written a few decades later, reports that Columbus's captains decided that they would go on for three more days, and then turn back if they didn't find land. Columbus's journal doesn't give this detail.
11th October: Land!
Judging by the actual voyage, they would have been reaching a point where the only safe option would have been to return. While they would have had plenty of hardtack and wine for the return journey, they would have been running low on other food, such as meat, and also fresh water. While Columbus - apparently confident that Asia was near - might have been reluctant to turn back, he might have had little choice, in the face of potential mutiny and supplies running low.