Can a Thorens 165 tone arm be replaced?

Like to do mods? Search eBay for "Thorens Rega mounting plate". You will find an inexpensive part which will allow you to put an RB300 on a TD165. If you go for it, the turntable will perform way, way better than with the original arm even when it was new.

You should be aware that when replacing with a Rega arm, VTA will not be within specs using these aftermarket mounting plates. You will have to use shims on the headshell and/or thicker platter mats. Some claim VTA won't matter much, I beg to differ.
You will have to do some grinding out of the metal on the subplate with a Dremel tool, so if you're not mechanically inclined this could be a problem. You will also have to rebalance springs as the Rega arm is heavier.
So yes, you can mount a Rega arm, installation is not exactly easy, and optimum performance from that setup is not easily achieved. Still, if you are mechanically inclined and like to fiddle about with mods, I would say go for it.

Thanks much, Sns. VTA not within specs... from what you say, that means the arm mounts too high in the Thorens plinth, is that right? You can shim up a Rega arm from below, but lowering it is more difficult if the plinth is already low. (Yes, VTA is important IMO.)

Yes Tobias, that is correct. I've modded my mounting plate by grinding a bit off the mounting legs, lowering the height, but still a bit off. Grinding off anymore will bring about mounting plate/plinth interference.
I wanted to install a Riggell VTA adjuster, but its a no go without shims in headshell or thicker platter mat (no platter mat will do it alone). I have concluded this arm cannot have correct static VTA without the shims or turntable mat, ie. no adjustable VTA device can work in this setup (you will only go higher with arm) unless you are willing to deal with lots of shims. Shims are too much of a compromise IMO.
One mod that would allow adjustable VTA would be machining the base of the Rega arm, allowing it to sit lower on mounting pad.

I think $100 is too steep if it isn't working. I think you should look for a better deal. You are going to spend $100 on the table, and another $300-$400 on the arm and adapter. You might as well look for a Rega P3 2000 for about the same price. The P3 2000 is better sounding than the td165, td160 and td145, IME. You have to move up to the TD125 to beat the Rega.