Assuming you use the standard srcds_run Linux script, it should restart within 10 seconds.
From my small experience of running tf2 servers I remember that you would need to reboot the server for it to kick off updates.
I did all the campaings and was kind fed up with it, but being able to choose my path and complete it with friends means I may do it this time too.
Pyro Jetpack - I said many times Pyro biggest hurdle is being an attack class with no range and no mobility, forcing him to either lose time going longer routes, or dying in the spammy main road.
This has helped a lot of users fix this problem because rubberbanding in tf2 is mostly related to your network connection.
Many users have reported fixing rubberbanding in tf2 by using different network enhancement utilities out there.
New weapon skins - If you really wanted to use X skin on Y weapon, this is the udpate for you. I could bitch about weapon skins looking silly but let's move on...