UPS/PSU question

I've got a new computer coming soon and have a few questions.

I've got a 375 watt UPS currently and the recommended PSU for my pc was 350. I chose a 600 watt just in-case I want to upgrade in the future.

My questions are:

1. Is this even going to work?

2. Does the UPS only provide 375 during battery usage? IE. It lets it pull as much from the wall and then when the wall stops giving power it actives the battery.

3. If number 2 is not true, when I get up to maximum usage is this going to cause problems?


Thanks in advanced