Some setups will turn the single coils into Icepicks but the Cybertwin should be pretty good with them though. Less gain, more mids. Depending on the music you want to play that may not work.
The Cybertwin may be a modeling amp, but the front end is analog. The entire amp reconfigures across a few boards. The effects including the EQ are digital but the Drive section is analog tube. It's not a buffer either its really a tube preamp. You should be able to make it sound damn good at reasonable volumes but at band levels the poweramp can be overwhelmed. This combined with weak pickups can certainly get harsh sounding.
Sometimes, A Strat just is not the right guitar.