Is certified translation of diploma an absolute necessary? I will apply for a Ph.D. position, and the university is asking for an English version of my transcript record and diploma.

My diploma/transcripts records are in French and the cost of a certified translation is enormous.

Is it possible to send non-certified translations? I would, of course, precise that they can ask for a certified one if necessary
Only they can answer the question as it is their rules that apply. But I think you propose a good solution. Send them a "faithful" translation that you can prepare at little cost. Offer to send a certified copy if necessary, but mention that the cost of such a translation is high. 

But you might also be able to have your university provide an English language translation or even to assure the recipient that your translation is accurate.