Can't see why not although any training you do between now and then will be limited. You need a couple of weeks rest now and then a decent taper before the next so you've really only got a 2 week window to get any key runs in.
I ran a half marathon pb 2 weeks after running the New York marathon so it's achievable.
I also think you need to work out what went wrong at London - cramping at 16 seems very premature. Were all of your long training runs run at slower than marathon pace?
Personally, I'd keep the training nice and easy over the next couple of weeks (maybe keeping the cross-training up) and see if the shoulder pain clears up. Will you have the cortazone injections before the marathon?
If you can somehow get a 16-18 miler in (pain free) before the beginning of April you should be able to get round.
One thing I would say is forget about any pre-conceived time targets you may have. I've made the mistake of not adjusting my time target following a 4 week injury and it turned London into one of the worst running experiences I've ever had.
At the end of the day you need to enjoy it. If you can't do that because of the pain then there really is little point in running.
Like you, I questioned what tactics I should use in my first couple of marathons. My club coach gave me sound advice which I've stuck to ever since.
From the start pace yourself consistently for the sub 4hr. Like others have said your 1/2 pb suggests this is a very realistic target.
If through 13m you're feeling good - stick with your pace If at 15m you're feeling good/strong - stick with the planned pace Same for the 18m mark - stick with the pace At 20m the race begins, you're feeling good so have a little think - Can I speed up? At 22m if you're still feeling good - Go for it. Get home as quick as possible.
In my last 3 marathons I've run 2 negative splits doing this and both times I've felt as though I had more in the tank at the end - Trust me this is one of the BEST feelings in the world (which inevitably makes you sign up for another marathon the following year as you're sure you can beat last years time). I've also found that this tactic breaks up the miles between 13-20 into bite size chunks.