Not impossible but it does say something about your work ethic. Lets say you have two applicants, you and one other person who applied in april, went for interview in may and is willing to start just after the exams. Of course not to say that is wrong and theres nothing bad about taking a grad trip after your studies but you hafta keep in mind the competition (note not only from your local uni peers, but from beyond our shores as well) and the general sentiment today that grad trips or more or less just outlandish holiday trips devoid of any qualitative significance.

Besides all job forms require you to put in a start date. lets say you put may/june and then go back on your word then it isn't very good nor ethical isn't it. and mind you although there are numerous employers here in sg, bad word does travel round pretty fast (dunno how it happens though, i'm not a hirer :P).