I guess it depends on the end game.
Many grad schools can suffice.
Not the same, but this sort of thing comes up a lot in the premed forums. Does the undergrad name matter for med school acceptance? Does the med school name matter for residency acceptance? If the end game is to be a “just” a successful practicing physician (which is probably 99% of docs), then the answer is no. Top stats from any good school is good enough for most/all med schools. Top stats from any US med school is good enough for most/all residencies. If your goal is academic medicine, then going to a better undergrad can help (i.e. Top 100ish). Getting into academic med usually means going to a top 50 med school (there are about 50 with MSTP programs). Getting into a tippy-top residency means having tippy-top stats, and being from a top 25ish med school can help because of the research opps that the student may have availed himself. Residency directors know that and appreciate that.
Applying the same thinking to the OP. What is his end game? Certainly Bama grads are being hired by some of the big names: Google, etc. Is his plan to go right from undergrad to grad? We’ve seen Bama COE grads go right from undergrad to Stanford, MIT, Berkeley, etc. Or is his goal to work a bit and then pursue a grad degree?