If you're using the free version of MBAM, then no, it will not prevent infection. Avast will, if there is a signature for the malware in the database. If there is no signature, then Avast may still alert you through the behavior shield, heuristics, or the auto sandbox feature that something seems wrong.
I think the combination of Avast and the free MBAM is pretty solid since if you do get infected, MBAM is an excellent removal tool for the vast majority of malware. Only certain types of malware may require the use of other things like AswMBR. The experts in these forums can fix just about anything that could happen so rest easy.