Yes, the Wein cells do work quite well, and they have a fairly stable voltage right around 1.35 VDC; that is what the circuit was designed to use. The only real criticism I have heard is their relatively short life. Some do report longer life with them if they put a new piece of tape over the little hole to keep air out when they put the camera away.
The common alkaline batteries may not be a good choice. Their voltage is constantly changing as they discharge and the voltage goes over a wide range doing that. The light meter keeps changing while the battery is doing that. A better choice here is the Silver-oxide battery such as the SR-44. It has a higher voltage, but its discharge curve is almost as flat as the old 1.35 VDC Mercury Cells, but the AgO cells are 1.50 to 1.55 VDC, until they hit the knee, and then they go down very quickly. This constant voltage thing really is not a bad thing. The Schottky Barrier Diode in the MR-9 battery adapter provides just enough voltage drop with the AgO battery so that the camera light meter happily thinks it has a PX13 or PX625 in it again.