Cheap batteries generally have a higher tendency to leak, discharge faster when not in use, and may not give your flash enough juice when the need arises, and this reduces your effective recycle rate. Over time the replacement cost of these batteries will probably outweigh your initial investment in a good set of rechargeables.
Just think - if you use and discard 4 cheap batteries after a shoot, or even 4 good alkalines like Duracell/ Energizer after 2-3 shoots, how many times can you do that before breaking even with say, 4 Sanyo Eneloops which can be recharged 1000 times. :think:
You can have a read of user experiences on said rechargeables yourself, just do a search on "Sanyo Eneloop" or "Maha PowerEx" in this forum.
Oh and yes please remove your batteries from the flash after shooting. I have had no leaks with my set of rechargeables though, probably good insulation and sealing.