yes, the thinner you go the more likely air is to seap out and the greater problems you will have. It will also vibrate alot. If you go to thin than the wood could not withstand the air pressure and your areas with sealant could start to seperate. Stay in the ballpark of 5/8" to 3/4" to 1" MDF. Medium Density Fiberboard.
not that pat, its that thin wood i.e. 1/2" and less will flex greatly especially in sealed or bandpass boxes with the air trappe inside being compressed and decompressed at great levels of pressure
3/4" MDF should be fine, but even that flexes so often times people will use internal bracing to prevent flexing, and this will also give more sound, making the box more effecient