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
Yes, you can if the feeder length is right. It should be around 1/4 of the operating wavelength or any odd multitudes of 1/4 (i.e. 3/4, 5/4, and so on). For example, if the feeder length (measured from the feed point to the point where it touches the ground for the first time) is in the range of 0.2 - 0.3 wavelength, you can do quite OK without a current balun (a.k.a. RF choke). Common-mode current will be low and you will not experience any negative effect due to lack of the choke. Examples: 80 m band dipole hanging about 20 m above ground level 40 m band dipole hanging about 10 m above ground level
However, if the coaxial feeder length is closer to even multitudes of 1/4 WL (that is 2/4, 4/4, 6/4, and so on), large common-mode current will be excited in the feeder.
In case of multiband antennas, achieving the "right" feeder length is often impossible.
If you have access to the ARRL QEX magazine and want to learn a little more, you may want to read my article "Designing antenna systems for low common-mode current in coaxial feed lines" that is supposed to be published in the July/August issue of the QEX. 73 SP3L