Not really.
Base on years of using and cleaning guns for hunting and target shooting and from reading several hundred reports of gun cleaning "accidents", "gun cleaning accident" is polite fiction for "I shot myself (or someone else!) playing with my gun". Although, to be fair, some of them are suicides and possibly the occasional murder.
Normally guns only need cleaning if they have been fired or have somehow gotten wet or contaminated. The procedure to clean a gun goes like this:
1) Remove ammunition
2) Partially disassemble gun (depending on model)
3) Scrub a cleaning rod and brush through the barrel and chamber
4) Reassemble
Removing the ammunition has to happen, otherwise you cannot run the brush though the barrel because the ammunition is in the way. So shooting yourself while cleaning a gun because you didn't know it was loaded is like driving off without your car keys. Not too plausible.
On the other hand, it's pretty easy to have an accident playing with a gun, and apparently shooting yourself is deeply embarrassing so it's not uncommon to lie about "I was cleaning it". I don't know why the police accept this story, just a social nicety I guess.
Of course this story works best if the "accident" happens in the home. A surprisingly common variation in cases where the gun owner shoots themselves in a parked car or suchlike (often with a newly purchased gun) is that a "black man ran up/drove by" and shot them for no reason. Sometimes the assailant was "wearing black clothes" and/or "driving a "black SUV". The police tend to be more skeptical about this although not always. [0] [1]
[0] http://www.startribune.com/wounded-st-kate-s-security-office...
[1] https://www.nbcwashington.com/news/local/Police-White-Man-Bl...