Like the question says, can you feed a dipole with coax with no ill effects? Nothing else in the system, just the antenna and the cable.
If "ill effects" include common-mode current on the feedline, no.
You can of course just tolerate the common-mode feedline current. In some situations it may not matter.
You certainly can feed the dipole with coax without a balun at the feedpoint, you will be able to work stations that would not be good on the dipole alone. The downside is that the noise level of the whole system dipole + coax will be higher. As the coax will radiate and also receive signals you will have a very different "radiation pattern" than with a balun at the feedpoint.
I suspect many of us "old hands" used to just attach 50 Ohm coax to a dipole before we learned better. You can use a 1:1 balun or "line isolator" close to your rig to reduce the amount of noise pickup etc but this will not be as effective as a 1:1 balun at the dipole's feedpoint.
So, it's try and see, if you like the sort-of dipole then OK, if not use the balun at the feedpoint and turn the aerial into a real dipole Vy 73 Tony G3ZRJ