I'll have to pipe in since this is my area of specialty.
To the OP:
Not all guns leave stria behind on the bullet (or casing) that are high enough quality for a positive association or a "match". I have personally test fired weapons, and looking at the test fires produced by myself, they was not suficient quality/quantity of correspondence between test fires produced sequentially for a "match". Secondly, unlike DNA and fingerprints, the marks a particular firearm will leave on fired bullets and casings will change overtime. This is due to continued wear & tear on the firearm, as well as possible damage/abuse to the firearm.
As far as if a match between an evidence bullet/casing and a test fired sample being enough evidence for an arrest that's a very difficult question to answer. My first question back to you is how is this match possible? Where did the test fire come from? Was it a firearm that was seized from a suspect during a search warrant? If so then yes possibly it would be enough evidence to arrest the person who was in possesion of the firearm. There is no sure-fire (pun intended) was of knowing who the owner of a firearm is. In the United States (except in select few states) firearms do not have to be registered. Sales receipts between a licensed dealer is required, but if that initial purchaser (non-gun dealer) then goes and sells the firearm, there is no requirement for any type of background check/tracking system.
If the firearm is a "found" gun, test fired, and a positive association is obtained using an automated database system (see NIBIN at the ATF website), then who do you arrest? You would have to prove that the original purchaser was still in possession of the firearm at the time of the crime- see above paragraph for further information.
There are only two states that have a system in place where all new firearms are test fired, and entered into that specific state's computer database system. Federal law prohibits all new firearms from being entered into the national system, and common sense, logistics, and the actual science behind firearms identification prove that such a system would be fruitless at today's technology level. The first reason has already been touched upon. That is that the individual characteristics of that firearm change over time - and most rapidly after the first few shots out of the factory as the weapon "breaks in". The second reason is that a database that would contain every new firearm sold would be so huge, and contain exhibits that vary so slightly that the current computer technology is not able to differentiate them.
In support of the second posts comments the bottom line is that unlike fingerprints and DNA, firearms identification links back to the tool used, and not to the person who pulled the trigger...it might be possible to get fingerprints or DNA off the firearm - but then we are back to someone who touched/came in contact with the firearm but not who pulled in the trigger in the crime.
If you have any other questions, feel free to post back.