Parties will mostly be at weekends, as will the school fairs etc, so you will meet other parents.
If your DC's get involved in school clubs, they may not finish until 4.15pm some days - would you be able to get away in time to collect from these?
Most of our school plays had an early evening performance.
Similarly, I hardly did a normal drop off, but dropped at breakfast club for my DC's entire primary school career - was still at school, so I felt involved. Often the teachers were chattier at 7.30am as they had their morning coffee!
Joining the PTA is probably the last thing you need if you are spending all day I'm a school, but helping out with the school fairs for an hour is a very quick way of getting involved. Applying to be a governor is probably too much, but most of my fellow governors are working full-time, and know more about the school than 99% of the parents.
Although I did pickups, I could never make a morning assembly, never did shared reading etc. The head teacher told me that she heard my then 7 year old tell a friend it was because I was very important with an important job, and that made me special. That actually meant more to me than listening to a recorder concert.
And, the obviously most important part of their school experience is what they tell you, over tea or in the bath. It's their perception which is the key thing.