Our pittosporum bushes are well established and our gardener made a huge mistake but trimming too close to the main trunk along the bottom. We live in Texas and the spring growth has already passed.

Will it come back or are we better off replacing with a 15 gallon pittosporum?

Pretty sure it will sprout from just below the cuts. I think your desired 'look' decides whether to live with this and shape new growth, or replace.

I'm thinking about giving it 5 months to show signs of growing back and then having it replaced with a 15 gallon bush of the same type if I don't see any new growth in that area. Do we think that's a reasonable amount of time?

I think you'll see new buds in a month or so, and by fall have an idea of whether you're liking it or want to replace it altogether. Seems like a good plan to me. I should probably admit I've never grown one, but am basing this on general shrub experience.