Of course you can brush after using whitening strips! Most use the same bleaching compounds as "whitening" toothpastes.
Interestingly, you get more bang for your buck if you brush beforehand. It makes sense, scrubbing off any excess substances that would absorb whiteners, as well as creating a more even surface for the strips to work on.
There was a clinical trial done by R.W. Gerlach, et al. about this "Impact of Prior Tooth Brushing on Whitening Strip Clinical Response":
"According to crest, you should not brush immediately before applying the strips; but after applying strips, it is fine to brush gently"
Here is the Q and A from their site.
Q. Can I brush my teeth immediately before using Whitestrips?
A. Do NOT brush immediately BEFORE applying strips. To avoid gum irritation, allow for some time to pass after you have brushed your teeth to apply strips.
Q. Can I brush my teeth immediately after using Whitestrips?
A. Yes, after using Whitestrips, you can brush gently.
For more information please refer to the related link.