To access a MDB file you need something called Jet which is a database engine that access makes use of. Jet comes with nearly every PC (I believe there are some 64-bit versions of windows without support however).
So yes you don't need access installed. However I'd really really suggest you consider using
Sql Express it doesn't come with an UI building tool, but it sounds like your not looking for that. Its scales miles better than Access/Jet, its more realiable, and faster. Plus it's just a limited version of the full Microsoft Sql Server 2005 (the limit is 1gb of ram & a maxium of 2Gb of data a database).
akakjs