The simple answer is no.
This may sound obvious, but 'open' is 'open' and 'up' is 'up' - so 'up' cannot mean open.
You'd only say 'I can't get the window up' if, in order to open it, you literally needed push it upwards - as with a sash window. If you said 'I can't get this jar up', I'd think that you were trying to put it on a very high shelf and couldn't reach.
All of our phrases with 'get'+ physical object+ x' are usually literal. Sometimes the x is an adjective.
Here are more examples:
Can you get this door closed?
You need to get this question right.
Try to get the children quiet.
I can't get this picture straight.
Sometimes the x is an adverb. In the case of 'get + object + up', it usually means succeeding in putting something in a higher position. For example, 'I spent all morning with a drill, hammer and nails, trying to get the kitchen shelves up. It took ages, because the walls are so uneven. Anyway, they're up now.'
Just curious.... what made you think that 'up' could mean 'open'?