Sets and models being reused and redressed is one of the main reasons Paramount spent less money on Star Trek II and III combined than they did on Star Trek: The Motion Picture. Also, despite having vastly superior visual effects to the film that preceded it, TUC cost 10% less to make than TFF, mainly due to using redressed TNG sets wherever possible. Nemesis cost $10 million less to make than Insurrection, because of the much smaller amount of location shooting the script required.
So yes, given that they no longer have to construct the Enterprise sets and CG model from scratch, it should most definitely help with how far they're able to stretch Star Trek XII's almost inevitably larger budget.
I don't think we need to fear Paramount pulling a budget cut on Star Trek XII. Star Trek's production budget of between $120-150 million was average, or perhaps slightly lower than average for a major studio blockbuster, while its financial performance has been considerably above average.