Your typical audio interface's "Hi-Z" input will not be as high-impedance as a guitar amp, but high enough to not matter
most of the time.
Oddly, many audio interface manufacturers seem reluctant to come right out and say what "high impedance" means on their products, so I've seen few specifications for them. I would expect, however, that it'll be at least 10K ohms. A tube amp will be 10x that.
So, as I suspect you suspect, there will be a little more loading on your guitar's pickups going straight into the interface compared to going into your Fender Twin. It's one of the reasons DI boxes are used when recording direct.