Any plane flying near a field with a published approach , even when crossing overhead at 90 degrees should be on frequency with the tower/radio, simply because 90 degrees means nothing. A plane going around could wekk cross you path at between 300 and 1000 feet.
Not being on the frequency is plain dangerous
Not necessarly. Especially so if there is no radar, and a radar service is available elsewhere.
I would always choose a radar service over a non-radar service.
dp