Sure we would, the universe couldn't collapse faster than light and light travels the same speed for all observers irrelevant of their motion.
I think the two keywords in my statement at the top is 'Just imagine'! :P
In all respect, whatever we see in the universe is in the past, and if it did start collapsing, we wouldnt know about it until well after the collapse had begun... For all we know, it could be collapsing right now.
I'm in a position where I do generally except theories as they stand, but the universe is such a weird place that the underpinning of how we 'think' the universe works isnt or wont ever be actually right, well, for a long time yet. So in my view, theorys are what they are... just suggestions backed by maths which tend to usually have flaws but are good enough for here and now.
And when it comes to subjects like this, I generally do what Czar mentions and pushing my own thoughts aside, would back Einstien and Hawkings... simply because... I'm only a plasterer! :D
Dabz