Color me extremely skeptical.
I was born and grew up in Houston. All my family are still there, so I visit 2-3 times per year. People who've never lived there sometimes don't realize what a large a population center it is -- twice the size of Dallas. Yes, metro DFW population is slightly larger than metro Houston, but DFW is widely dispersed across two core cities and 11 counties, while Houston is much more concentrated in one core city and 9 counties. The Census Bureau dubs DFW a "conurbated" MSA (metro statistical area), meaning a bunch of separate metropolises, medium cities, large towns, and other urban areas lumped together. DFW has three urban focal points: Dallas, Fort Worth, and Arlington. Metro Houston has only one: Houston.
Getting such a large, concentrated population to coalesce around UH, with all the competing, higher loyalties to Houston's pro teams, is a very tall order. To complicate matters, Houston is the most diverse large city in North America (according to Census Bureau's Diversity Index), with more ethnicities represented and more languages spoken (about 145) than even New York. In most Texas cities, you hear only two languages: English and Spanish. In Houston, add Chinese, Vietnamese, German, French, Arabic, Urdu, and a few score others.
How do you get all those disparate groups aligned behind a single college team? Worse, at an institution that most of the city routinely ignores? The only university I can think of that gets even less attention from its home city is SMU.