The tension will matter. Look at the pic again ... if the spring is refitted on the bracket with the mechanism in the "almost down" position, when it winds the window up it's going to take all the tension off the spring and eventually lift it out of the bracket. In the middle, there'll be a position with zero tension on the spring when it can easily fall out.
I think the correct way would be to reconnect the window motor once it's removed and wind it all the way up, then refit the spring, then wind it down again. The only sure way of verifying this is to strip down a working door and window motor - which I'm not about to do!
The other thing I'm worried about is that this motor (my passenger door) seems a little weak anyhow, and might struggle even with the weight of the window glass to lower the window and wind the spring up.
Think I might just remove the spring altogether ... it had been working without it for ages anyhow!