My bf of 2 years doesn't have a whatsapp profile photo and is in the police. And he has a very restricted social media which does feature me but would be impossible for strangers to find. He's lovely and hasn't cheated and I know him well enough that it wouldn't be his style. I work in a City type job and plenty of people cheat here too. I've also worked in the public sector and everyone was shagging everyone in my division. In fact, every profession is rife with it.
However, the shift work is a killer and you do need to be understanding of it, and comfortable spending a lot of time on your own. So only if you're a very independent person who can cope with an alone weekend for example because he'll be working, or doesn't mind going to events alone without him. Also need to be very secure yourself, my bf has female partners on the job he spends hours with everyday and it doesn't faze me at all because i trust him. But I can see that if you're not prone to trust, it can be a problem.
Regarding wanting to come off it, who knows. It is certainly possible someone he arrested is on there, or he could be a liar. But he could be in any job and be a liar. My bf has had instances where people have 'made' him as a copper, because they had some run in with him, and tried to get aggressive/pick a fight. And it has always worried me that they might be able to find out who i am/where i live and harass me too - so I encourage my partner to take online security very carefully. Any job where you come across that number of dickheads who hate you, it pays to be discrete.
The positives of his job are that he is incredibly calm under pressure in life, quite emotionally intelligent because he of all the various types of people he comes into contact with, has a certain confidence when we are out and about that makes me feel safe even in risky situation, has a stable profession not prone to redundancy like my industry, and his shift work means he can pick up the slack on days that i'm working. Also I am very proud of the work he does! However, not every officer is like this, so i can't generalise.
Obviously, cheaters/scammers are also discrete. So meet up with him, and trust your gut. You'll soon get the measure of him.