Yeah it does. Adobe has a lot of active script support, including java script for example, which can be exploited. If a software can’t interpret those scripts at all and simply displays plain text, that means malware won’t be executed.
And since Adobe Acrobat / Acrobat Reader are the most common pdf viewers out there, they are a natural target for hackers as well.
I genuinely don’t know, I have set my browser to download pdfs by default and only open them with Sumatra. There might be a scripting layer active in the browser as well though, quite possible.