The short answer is yes, the long answer is depends.

The background

• Are you shooting full body? It is a little more difficult to make a smooth background.

• Do you have enough space between your background to the subject? If you have considerable space you can put more power to the background light or use a big difused light.

• Does the background light has enough power and amplitude to fill the background?

• Do you have enough space between the background and the background flash to have an even ilumination? You can use one light in some cases.

• Does the main light spills some light on the background? It can help to smooth the background. The same as the next question.

• Is your studio painted in white? This last two options helps for a high key portrait.

Main subject

• Is the white reflector big enough?

• Can you put the reflector it verey close to the subject? Probably remove it later in post pro.

• Is the main light big enough, in the right angle and distance to spill light to the reflector?

• Can you use aditional white boards to fill the subject?

• Are you limited to use a white reflector? or Can you use a silver one?

• How much shadow do you want on your subject?

My recomendations

• Play with your lights, have fun and make tests considering all this variables: Difussion, distances, power, ambient.

• You can use a second flash as a background flash and a rim light for example.

• Use swich between one or two flashes for the background.

• Bounce the flashes all over a small white room, or make a light tent for a full body.

• Make a dramatic shadow with a single main light but white background.

• Use some natural ambient light.

• Again, play and have fun.