According to what they've said so far, yes, it will allow it so long as the app developer makes the necessary changes to make it work – supposedly these are very simple so most apps should allow multitasking very quickly.
Funnily enough though I've found the lack of multitasking a lot less of an issue than I thought I would having come from a phone that did do it. Still looking forward to it when it's realeased. Frankly though I can't believe it didn't do cut & paste earlier though. without that, it really must have been a pain – I use it all the time and it seems to me that the iPhone was completely crippled before that (which is one of the reasons I didn't get one then).