There are a couple of factors that would determine whether this configuration would work as intended. I list the problems in order of frequency, as I encountered them.
The maker of the adapter. Many of the cheaper makers on Amazon (approximately 80%, I'd estimate) make adapters which cannot support a high traffic through their adapters. When their adapters get overloaded, the image freezes, and depending on the adapter, can be refreshed in one of several ways (e.g., minimizing and then restoring the window in question).
The speed of the USB. USB 2.0 can support at most one monitor at a 1024x768 resolution. Maybe if the maker is ingenious, you can get away with something a little bigger. Not a lot. USB 3.0 can handle two monitors.
The CPU bandwidth. A lot of times, the limiting factor with running two monitors off of a USB 3.0 is, that it takes away from the bandwidth of the other USB's connected to the motherboard; and if you saturate the connection, the display suffers. I found that buying a dedicated PCIe card (or PCMCIA, etc.) to handle the USBs allows the CPU to receive this information more efficiently, and therefore allows more monitors to be connected at a higher resolution.
Bottom line is, since you have an adapter already, you can try it out, and post the results here.