Parking isn't particularly easy, especially if there are a load of you, although you may be able to leave cars and trailers on the slip itself subject to tides (it's very wide!).
The tides aren't too good that weekend -- it's spring tides which means that there will be strong currents. More importantly, it's difficult to launch and recover at less than half tide which will mean before ~08.00 or after ~15.00
2 March tides for London Bridge:
Spring HW at Putney is London Bridge +~30minutes
Spring LW at Putney is London Bridge +~1hr 40
2 March tides for Putney:
Having said all that, the SIB brigade should be fine at any tide because they can just pick their boats up and carry them. It's only trailers that will have problems at low water . . .
By the way, the picture on www.boatlaunch.co.uk
shows the narrower of the slipways -- there is another just upriver opposite Chas Newens Marine which may be easier.
Also on the boatlaunch site is says the speed limit is 4 knots, but it's 8 knots (Geoff, are you listening?
Anyway, I hope I haven't put everyone off. Have fun!