This is a US-based answer.
Theoretical computer science is indeed less well-funded, but it is also less popular, and the effect of this on graduate admissions is complicated. You should also consider the effect on your eventual chances for jobs after you finish your PhD.
The main effect of TCS being less well-funded is that many lower-ranked, smaller departments do not have anyone in TCS at all and have no plans of hiring anyone, because the people they can hire in TCS would not be able to get funding. If your record can only get you admitted to, say, University of Georgia, then you are out of luck; they don't have any faculty with primary interests in TCS as far as I can tell.
On the other hand, if you are competitive for admission at University of Illinois at Urbana-Champaign, then you probably need a slightly less impressive record to get admitted in TCS, because they have a lot more applicants interested in AI/ML than their faculty can advise, whereas they only have somewhat more applicants interested in TCS than faculty availability.
You should make sure you are only applying to departments with several faculty primarily interested in TCS, but if you are doing that (and competitive for admission in those departments), then mentioning an interest in TCS probably helps your application.
You should also consider the other end. Once you get a PhD, only the best researchers in the TCS will eventually get faculty jobs at research universities (or research jobs in industry), whereas merely good researchers in other areas frequently manage to get faculty jobs.