MPO...I wouldn't do it but I tend to err on the side of caution when it comes to my system. Here's a long and interesting discussion on the subject that you might find interesting.

http://www.sevenforums.com/backup-restore/177278-can-i-use-my-computer-while-imaging-my-hard-drive.html

Other things being equal, if you're just surfing around it should be fine, as you're not changing any important files - which surfing around shouldn't be.

I suppose if you had a very underpowered computer, and viewing some web page with too many tabs open - or some similar scenario presenting a big cpu challenge - that caused the cpu is stutter or stall - then you could run a risk. But other than that, it should be fine.

If you were actually editing a file that's set for backup, there's a fairly good chance it would be locked while editing, thus, not backed up. Or at least, the edited changes wouldn't be backed up.
Btw, imaging is different than file backup in a non-trivial manner, but even then, just surfing around on the internet shouldn't make any difference.

Windows here makes a scheduled image daily on my laptop to a 2nd hard drive that replaced my dvd. They're both ssd's and takes something less than 2 minutes, maybe 3 minutes every two weeks for a new starting full image.

I never pause for it and mostly don't even notice when it happens.