Potentially. No harm in it.
Looking longer term, if you were progressing you'd be likely to move onto one of the chartered qualifications afterwards if you wanted to open more doors.
You could equally well spend the time starting the ACCA qualification. On the face of it it sounds like you'd be eligible for direct entry without AAT.
You don't need to be in a training contract to start your exams and can do them at your own pace. It's pretty flexible now in terms of how many exams you do how often etc. Self study, online study, classroom study. BPP and Kaplan are the main providers.
You have ten years to complete all your exams and achieve your practical experience in order to qualify, so you wouldn't be up against the clock and could take a pause or multiple pauses. You need 3 years practical experience on top of the exams to qualify, but you can gain it afterwards or alongside.
Having started yourself on ACCA does make you more marketable. I've worked with people who started their exams in an entirely unrelated role as a way to get their foot in the door of an accountancy job, and then absolutely flew in terms of progression.
There will always be a transition between what you learn in the classroom and learning the job itself (hence the practical experience requirement to qualify), but if you're capable and determined in your studies then there is no reason you won't be able to and employers will look at how you managed your exams - so if you have exam passes under your belt already that is a positive. Employers tend to look favourably (in my experience) upon prospective trainees who've already shown the commitment to study and pass exams in their own time before landing a job.
ACCA also offers a technician qualification (which is what AAT is) that you can do before moving on to ACCA - CAT.
I don't think it's a bad idea at all. Just make sure you fully research and understand the different accounting qualifications, what they mean (eg difference between a technician qualification and a chartered qualification), and where they'll take you. As well as what you want to do with them afterwards!
AAT courses are offered a lot in colleges so there can sometimes be a perception that it's THE way to become an accountant and that once you have AAT you're fully qualified. Whilst it's absolutely a worthwhile qualification, it would also be a much longer path if you wanted to go all the way through to achieving chartered status. If you don't there is nothing wrong with that, but I would encourage you to make sure you understand the sector and all your options before you commit to one qualification. Some people want the experience of one of the technician qualifications before moving on, others don't. There is nothing wrong with either choice
Technician - AAT, CAT, ATT (tax specialist)...
Chartered - CIMA, ACCA, ICAEW, ICAS, CTA (tax specialist)...
There are other qualifications, but those are the main ones... With the exception of CAT, these are all from separate institutes (CAT is offered by ACCA). There are also other qualifications on offer by them. The qualification you choose really depends on what you want to do with it.
For example, CIMA is more for people who want to work as part of the accounts function in another business (eg being part of the finance team at M&S), ICAEW is traditionally for those who want to work in an accountancy practice, and ACCA is suitable for both.