Common mode current occurs due to coupling between the antenna and the coax shield, so if you place the choke at the feedpoint, you break the circuit and most of the common mode current will be blocked. (The circuit is from the antenna, though the coax, and back to the antenna via RF.) You shouldn't get any significant amount of common mode current further down the coax.
However, nothing is perfect, and some common mode current may leak past the choke, especially if it is at a nodal point. If this is the case, placement of a second choke somewhat further down the line (say, 1/8 wavelength velocity factor corrected) may hit a maximum and block more current.
Alternately, if you don't place a balun at the feedpoint, then the coax between the balun and the antenna can become part of the antenna and will radiate. If that length of coax is resonant (say, 1/4 wavelength), then this will have minimal impact on SWR shouldn't cause more common mode current past the balun. It will, however, change your radiation pattern, which could increase or decrease your gain, depending on the direction of interest. This is one way to soften the directionality of a beam where you want to get some omnidirectional radiation, or even add a band to an antenna. (For example, the carolina windom uses a 1/4 wavelength of coax with a choke for 10m.)
Placement of a choke at the transmitter might also help, but it only helps common mode from getting into the transmitter -- it may still be on the coax.
There are two primary reasons why we care about common mode current at all. First, common mode current on the coax in the shack is dangerous -- it means you are radiating in the shack, but also you could get RF burns from touching surfaces carrying that common mode current. Secondly, common mode current sourced from the feedpoint is power that is not going into the antenna, and may be radiating in directions we don't want and causing high swr. Other sources of common mode current should be negligible and inconsequential.