No.
That's the point. I never considered installing such application and the tablet isn’t rooted.
The only thing I can think of, is the first time I installed avast, AVG antivirus was present (it didn’t complaint, though). As far as I know, AVG doesn’t include anything more than the real-time scanning. AVG is gone for a long time to no avail.
I obviously have other (than avast) applications installed on my tablet. If there was something restricting access on my tablet, I'd know instantly. There isn’t.