Can I use a grey card and histogram instead of a flash meter for studio flash?

Certainly. A flash meter is really (mostly) just a way to trade money for time. In my film days, a flash meter could save me literally hours compared to Polaroids on a complex shot (which translates to days using wet-processed film tests). With digital, and especially if you have remote control of your flash output, the time lost to exposure testing is insignificant. It's still not quite as quick as a flash meter, but it's now down to seconds or minutes lost at most (which can still be a significant time sink for a full-time working pro).

It will mean filling the frame (or at lest nearly filling it) with your exposure card, whether that's an ordinary grey card or a black/grey/white card. You'll need a lot of pixels to make a useful peak in the histogram, and if the card is too small in the frame, you may not be able to pick out the peak(s). There is no need, though, to try to guess where two stops up or one-and-a-half stops down fall on the tiny, uncalibrated histogram at the back of your camera; you just need to know where "normal" lives.

In the specific case you mentioned — overexposing a white background by two stops — you'd simply close your aperture down two stops and use the histogram to meter for "normal". When you open back up to your main subject exposure, the background will be two stops over. It only gets a little more complicated when you want to measure underexposure, and then only if you can't actually open the aperture far enough to measure — in that case, you'd need to adjust the camera's ISO higher by a corresponding amount (leaving your aperture at the main shooting aperture), then adjust flash output or reflector positions until you get a "normal" histogram. Again, once the camera is set back to its main subject shooting settings, the light you measured at "normal" will be underexposed by the desired amount.

In all of these cases, a tri-tone (black/grey/white) exposure card will be somewhat easier to use than a grey card, simply because the three peaks are easier to visually centre than the single peak of the grey card. And in all of these cases, you'll need to figure out where, for your camera and card, the exposure card's histogram peaks need to be for a "normal" exposure. But a little bit of testing up front to "clabrate" the camera/card system and a little extra time taken when setting up the shot will get you the functional equivalent of a flash meter.