If you're flying out 10:30 AM next day, I think you may have trouble. The check ins are long due the new anti terror regs:

They aren't that bad, BA for example recommend you check in two hours before an international flight.

if you have to be in Gatwick from out of London this would mean getting out of Victoria at some ridiculous time like 6 AM or even earlier. I am not sure what the Gatwick express is like these days (it used to be quite good) but I don't know what time the trains start.

The trains from London to Gatwick are some of the most frequent around...

The last train each day is 00:30 and then the first of the day is at 04:30, from 06:00 to 20:00 they are every 15 minutes, the rest of the time they are every half an hour.

http://www.gatwickexpress.com/view.asp?pageid=4

If you are in central London to see a play, then I doubt there's going to be many trains coming out of town to Gatwick at the time the play finishes. If it's a 7 PM start, and the play runs to 10:30, you will maybe only just get enough time to get out of the theatre and get a drink before the bars start to close: you'll then have to get the tube across to Victoria to catch the express.

Not true, he'll have plenty if time to make the last train. There are trains every half hour until 00:30.

Don't underestimate how awful public transport is in London at the moment - a large number of tube stations are closed due to safety issues caused by the Fire Brigade strike - you may find the tube station near the theatre is closed!

There aren't actually many stations closed:

http://www.londontransport.co.uk/tfl/strike/firefightersstrikemap.pdf

The station nearest the theatre is Piccadilly Circus, which is not effected by the strike. It's not far from there to Victoria, 25 minutes by tube even at the worst time of the day.