Is it possible that, if a segfault occurs after allocating memory but
before freeing it, this leaks memory (that is, the memory is never
freed resulting in a memory leak)?
Yes and No: The process which crashes should be tiedied completely by the OS. However consider other processes spawned by your process: They might not get terminated completely. However usually these shouldn't take too many resources at all, but this may vary depending on your program. See http://en.wikipedia.org/wiki/Zombie_process
If so, is there any way to ensure allocated memory is cleaned up in
the event of a segfault?
In case the program is non critical (meaning there are no lives at stake if it crashes) I suggest fixing the segmentation fault. If you really need to be able to handle segmentation faults see the answer on this topic: How to catch segmentation fault in Linux?
UPDATE: Please note that despite the fact that it is possible to handle SIGSEGV signals (and continuning in program flow) it is not a secure way to rely on, since - as pointed out in the comments below - it is undefined behaviour meaning differen platforms/compilers/... may react differently.
So by any means possible fixing segmentation faults (as well as access violations on windows) should have first priority. Still using the suggested solution to handle signals this way must be thoroughly tested and if put in production code you must be aware of it and draw any consequences - which may vary and depend on your requirements so I will not name any.