To give my opinion on wether it is possible to be aro and want to date, I would say yes but it mostly depend on the definition you give of "dating". I know that when I discovered aromanticism my reaction was : I can't be aromantic, I want to date someone ! But when I started going on this forum and really started to question myself and what I want, I discorvered that my definition of dating wasn't the same as how my friends. I Don't really know how to explain but when my friends dated somoene it was because they loved them romantically and only because of that. But this was never really a criteria for me ?
At the time I hadn't realised that, but now I don't know how I did to not see it before ! The fact that I wanted to "date" was more because of society expactation than anything else. For me, to have a happy life you had to go to school + find a job + marry and tada ! you are happy ! (well I really simplyfied it, but it was basically what I was thinking).
Now I know that my definition of dating is not the same as most people. For me dating is more like a meeting with friend that I appreciate a lot
I even have a friend on the aro spectrum and we always say jokingly that we go on date when we go to the restaurant or things like that ?
In addition to that, I also have date with my QPP (who is an alloromantic), and this does not mean that I am any less of an aromantic.
So my answer is definitly yes. Maybe you should question if like me you want to date is caused by amatonormativity or because you do not really have the same definition has anyone else.
(sorry for anny mistake or mispelling, English is not my first language)