A relationship like that is not something you can safely predict. The competition on google.com can be much more intense, for one thing. And then there's geo-located results depending on where the web connection is. Also there's the question of where your backlinks are located.
Still, it certainly might happen - the jump you've seen sounds like a very hopeful sign and it may well predict at least an improvement on google.com. Let us know how things progress for you.
In my limited experience, you could get "stuck" in the SERPs.
For one single competitive keyword, I get these SERPs:
UK - #3
Canada - #3
USA - #7
It's been that way for weeks for the first two; for the US, I've been shuffled between #5 and #8.
If Google scrutinizes competitive keywords more closely, and there's the greatest competition for Google.com searches, it could be a challenge to go higher in Google.com versus the other countries. It probably takes great IBLs from American sites.
I'd be curious to know what percentage of Google users search from the Google of their country. It seems Google automatically defaults to your country and you actually have to change your settings if you're not in the US to get the .com. Don't know how many people either a) know how to do that, or, b) could be bothered.
I have the opposite problem I am #1/2/3ish on .com but 3rd page on my local G. I am tempted to set my geographical region in the webmaster tools but im cynical. What if they drop my .com rankings, and my .co.uk doesnt pick up. Hmm...
It is actually quite strange this in itself as the site is very UK, with a majority of UK ibl (sorry slight hijack there)