Normally, yes. Firefox Beta and Firefox Aurora will detect your currently active profile and use it "as is", making whatever updates are needed for compatibility with the new version.

However, I have to say, there are definitely no guarantees, particularly with the cache. For example, if Firefox crashes, it may invalidate your entire cache and rebuild it from scratch as you revisit those sites.

Why is the cache so important?

It is usually not a good idea to switch exclusively to one of the development versions and abandon (remove) the current release.

Such development versions can fail at any time and some web pages may not work properly, so it is best to keep the current Firefox release and install development versions alongside of it with their own profile folder.

• http://kb.mozillazine.org/Testing_pre-release_versions

now as you people have told i am abandoning the idea of installing aurora but i still want to install firefox beta,i want to get involved more,so should i do it,please?!

and the cache is so important because it's 651 mb and none of it is worthless,my internet is slower,so having this much cache helps,i actively trim my cache of useless things so it's worth a lot.

A couple times I have installed the beta during its last 2-3 weeks of testing, so about 3-4 weeks after the latest Firefox release. I think by then the most severe bugs usually have been fixed.

I'm not saying that you shouldn't install a beta or Aurora version, just that it is better to keep to Firefox release and be prepared for issues and have the release with its own profile (don't run the same profile with different versions).

There can always be issues although they are less likely with the Beta releases.
It is a good idea to test out the beta version, so if things go wrong then you can file a bug report if necessary and have serious issues fixed before it becomes a release.