It is possible, but you will definitely face some obstacles while trying to sort things out, such as opening a bank account, subscribing for television or many other things. If you have a hungarian friend ask him or her to help you out when dealing with any of the above. Hungarians generally don't speak any other language, however Budapest is getting more and more an international city and most young people do speak English now, so there is a positive trend going on.
In a nutshell it is possible, I have many foreigner friends living in the city and they do just fine without knowing more than the absolute basics.
Hope it helped.