Yes and no.
In my previous situation, my ex was constantly accusing me of cheating or suspicious when I went out to clubs without him.  He was cheating on me the whole time.  
I used to snoop through his text msgs, email and call lists.  That's because I'd already caught him cheating on me once, and he used to get pissed off when I asked him why he would go out with his 'buddies', turn off his phone, and not come home until 7 am.  I felt I had the right because he'd already been proven a liar.  Turns out he was cheating again.
However, I was younger and inexperienced then.  I wouldn't bother with the accusations and the snooping anymore.  If they were acting shady or lied about stuff like that even once, it would be a simple GTFO.
				
			 
			
		 
			
				
			
			
				Live as if you were to die tomorrow. Learn as if you were to live forever. - Mohandas Gandhi