WP8.1 won't be hitting any devices, any time soon. April 2 is when WP8.1 is expected to be announced at BUILD. That's just the /announcement/, when the world gets and official peak at what's coming (rather than all of the leaks, which the folks at Redmond are not very happy about). It's also expected that the Developer Preview for Windows Phone 8.1 will be announced and/or unveiled.
So in terms of expecting a phone bought in March having it? No such luck: as far as Microsoft is concerned, they won't even acknowledge it exists. Try asking them about it, they'll say there's no such thing.
Even then, phones can sit on the shelf for quite some time, so it still likely won't have the latest software. I bought a Lumia 520 just a week ago: it was still rocking GDR1, so I had to update it to Black OTA.
As for when WP8.1 will become available for devices through normal distribution channels (I.E: carriers)? I'd hope it will hit 90%+ of devices before the end of 2014... But who knows? The carriers can be total bitches...