After reading up on Appel reactions a bit, it looks like CCl4 would work just as well as CBr4. Some thoughts on this, though:
I definitely like the idea of having a relatively mild way of converting something into a halide, but I think there would be a few problems.
Because PPh3/CCl4 forms a trichlorocarbanion, I think it would be best if the concentration of PPh3/CCl4 was kept low compared to OH-(CH2CH2-O-CH2CH2-O-)n-CH2CH2Cl (if my "X" group is going to be hydroxide). Since -:CCl3 can spontaneously form :CCl2, it would be important to give an ample opportunity for the carbanion to deprotonate the OH- group before it's allowed to become a carbene. I'm also concerned that the carbanion may do a nucleophilic attack on the chloro- group on my target molecule and form an unwanted side product.
I'm also wondering if the PPh3 would react directly with the chloro group on OH-(CH2CH2-O-CH2CH2-O-)n-CH2CH2Cl as well as CCl4. If it does, then the resulting phosphonium salt would probably end up dimerizing my product there. True, there's fewer halogens withdrawing electron density from the carbon on this molecule than there is on CCl4, but is that going to be much of a factor?