I've also lodged flight plans directly through it, and have never had ATC mention anything - although to be honest I don't know if doing so is part of their job.
It is very much so - protecting restricted areas is as important a job as protecting separation.
In CTA we need to actually separate aircraft that are operating under a clearance from active restricted areas (5nm clear by radar and all that). OCTA it's a pilot responsibility to remain clear, though if we are talking to you - ie you are IFR or receiving a VFR Flight Following service - we'll give you a friendly nudge if we notice your route going straight through (or very close) to an
active restricted area to confirm you're aware of it and are planning to avoid it in some fashion.
If you're VFR, we obviously don't know who you are, nor do we know exactly what you're planning to do (the radar tracks are not coupled to a flight plan if you're not talking to us). If we see a VFR paint infringing an active restricted area (or controlled airspace for that matter) we'll make a broadcast to find out who you are and what the story is - maybe you're lost, maybe you're under stress of weather or whatever - and whether you require any assistance. Paperwork will go in about it (even if we don't identify the errant aircraft) but that's to track trends and to see if Airservices can find out why infringements are happening, with an aim to improving education to reduce how often they happen again.
But that's completely by the bye if the restricted area is not active. In that case, fly in, around, through and over it to your heart's content. It's not active, it's not being used, it's all yours!!
The important thing for VFR pilots, though - and this applies even if PRD are not involved - is to be monitoring the area frequency and speak up if you think we might be calling you. It means we have information we think you should know - active PRD, conflicting traffic etc - not because we want to get you in trouble.