Yes, a light meter could be helpful in giving you solid, mathematically correct guidance in setting lighting ratios. Keep in mind, in cramped shooting scenarios, the degree of light fall-off is VERY rapid over the beginning of a "run"; as the distance the light has travelled increases, the degree of fall-off becomes more gradual. This physics behavior is due to a principle called the Inverse Square Law. The upshot is that, in close-range, short-distance set-ups, minor errors or minor differences in light level settings on flash units can cause TREMENDOUS over-exposure ( or major UNDER-exposure, depending on what is being metered or what is being exposed for).
In situations exactly like this one, in a small studio or temporary studio, where you want a white backdrop, one of the easiest ways to get it right is NOT to "add more light" to the backdrop fabric or wall, but to use LESS light on the foreground person, and to then exposure for the shadow side, to expose for the "face and body", and in that way, you can get the backdrop white, and minimize blowback by using LESS light than you might expect would be needed to get a white backdrop.
When you're in a cramped, close-distance scenario, where the flash units are very physically close to backdrops, or faces, the RATE and the ABSOLUTE degree of fall-off (or blow-out) is very,very,very rapid over the first part of the total distance. The first foot to the second foot can easily be a full EV value plus or minus (plus depending on if you're metering the highlight or minus the shadow).
What you want is a flash meter that meters incident light and reflected light. Both methods are used, incident to set the face value, reflected to determine what tonal value (blown-out white, white, 90$, 75 %, 50%, 18% gray, etc) ANY fabric or wall will be registered at. Meter the face with the incident dome, and use the reflected value to determine the tonal value the backdrop will render at. Sekonic makes some very good flash meters; a meter that reads both ambient light and flash pops is called a 'combination meter', although that specific nomenclature is seldom used these days.