From experience, it is not very easy to establish residency in that amount of time. I moved here from out of state with my wife in 2003 when she was still in college. She actually had to take a year off from school while we established residency. Needless to say, that was a tough year for her (and me).
If I remember correctly, it was something like 6-9 months that he must live here (This is only if he is independent). Also, if the primary reason that he is coming to Texas is for school, they will know. The only way to establish residency this quickly to my knowledge is for him to receive a Texas HS diploma and for YOU to move down here as well. This is probably not in your gameplan.
This is what happened to us 6 years ago. Even being married and completely independent from her parents wasn't enough.
As you have read below, there are very few bad investments when looking near campus due to their demand and "rentability". But, if your primary reason for buying is to establish residency, I don't think it will work in this situation.
Even an average condo purchase near campus is going to be relatively expensive compared to the rent you might pay. The difference between rent and mortgage may offset the tuition increase. I don't know the exact tuition for UT these days, but I assume it is somewhere around $4,000 per semester or $8,000 per year (or $666 per month).
If out of state tuition is about 3 X that amount or $24,000 per year (usually the case), the difference is $16,000. When you break that up monthly, you get a difference of $1,333.
You can rent a decent place near campus for around $600 per month. But a comparable purchase would run you around $200k. The monthly payments on such a loan assuming 5% down and 5% interest would be about $1,550 depending on taxes and HOA fees.
So let's compare:
Out-of-state tuition + rent = $2,599 per month
In-state tuition + mortgage = $2,216 per month
Certainly, there's a difference, but not quite as big once you consider all angles. You can buy cheaper condos but they are VERY small and most of them have been on the market for quite a while.
This all may be a moot point if you cannot establish residency. But, hopefully it can at least help put a few things in perspective for you.
Good luck, Ron. I hope it works out for you.