I'm a mountain biker thinking of getting a road bike for training.
Is the size based on the seat tube length like mountain bikes.
I'm 6'7 with long legs and arms. 38" inseam
Do you think I could fit on a 63cm since this seems to be the biggest available in the entry level bikes? Are there ways to adjust the handle bar height with different stems. etc.?

talk to a bike shop, they should be able to fit you properly.
you can adjust almost anything.

A standard size 63 is likely to be small for you. Both Trek and Specialized have models with taller head tubes, which makes it a bit easier for a tall rider to get a comfortable riding position. Ultra-tall frames are sometimes available on E-Bay for cheap, because there are not many 6'7" guys around to bid on them.

Talk to several bike shops about your choices. The obvious choice is to put an ultra-long seatpost and ultra-head stem on a size 63 or size 64. But, a frame that truly fits you will ride and handle better than a "too small" frame with extra-tall parts.

Thanks Alan
I just looked at the Trek website. Are you referring to the Pilot 1.0. The 63 cm has an 8.3 inch head tube.
Do you know of any mfg's that make a bigger bike?

Wow - you're really tall. I bet you never ever tire of hearing that.

I have Fuji (a 2006 Roubaix RC). They make some of their bikes (the low-mid range) in a 64cm. It had just enough extra length/height over the 63cm I tried that it was enough. I'm 6'5"-6'6" (seasonal fluctuation) with a 37 inseam. I have a simple comparison of the geometry of a 63cm Cannondale vs. 64cm Fuji. PM me your email address and I'll send it to you.

Just go to a shop that will fit you properly. You may not see a 63cm frame on display, but they do exist. I also saw a 66cm frame the other day: https://www.somafab.com/extrasmoothie.html

Finding the right bike may be a little lengthly if you have to order it, but the effort will be worth it.