Can a vice president who becomes president by succession be elected president for 2 full terms?

Yes, provided that he / she becomes President more than two years into the initial term.

The twenty second amendment to the US Constitution stipulates that a President is not eligible for re-election if they have served more than six years in office.

Gerald Ford, had he been elected in 1976, would have been eligible for re-election in 1980, for instance.

No President has served more than two terms since the adoption of the amendment, however.