Hi,
Not sure what you mean exactly.....
On most (all?) modern DSOs you can save screenshots and/or actual waveform data (once captured) to a USB drive.
But if you're talking about having the USB drive as the main acquisition memory (and therefor get a memory depth of 4G for a couple of bucks) then no, it doesn't work like that.
Your typical DSO captures tens of thousands of waveforms per second, each waveform cosisting of tens of thosands of bytes (depending on scope settings of course). These bytes needs to be continuosly "streamed" to memory (and from memory in order to build the waveform you see on the screen). For this you need fast RAM "tightly" tied in with the ADC's and main processing CPU/FPGA etc. Having FLASH memory on USB won't work.