I suppose my question would not look at the backup itself, but if you feel comfortable using a drive that is already having problems to make one. Maybe it would not hurt to try, even if the final result was not acceptable, you could still just reinstall and you might be able to pull old files out of the backup.
Do you have an external drive you could try a Windows image backup right now? If the drive is going bad, the sooner the better.
I have always used the built-in imaging utility, but it is restricted in what it can do. If you plan ahead and resize partitions and move some data to other locations, you can usually get it to work.