Radar - How to keep IF constant?
To answer your question: No, you can't generate your local oscillator that way.

The output of the first mixer will have both sum and difference frequencies in it. In other words, in addition to a signal that runs from 2201 to 2601 MHz, you'll also have a signal that runs from 2199 to 2599 MHz, and there's no way to eliminate just one of those signals.

It isn't clear to me why you want an additional frequency offset anyway. The usual idea with this kind of radar is that the reflected signal already has a frequency offset from the current transmitter frequency that's based on the round-trip delay between the radar and the reflecting object. The beat frequency gives you a direct measurement of the distance to the object. And if it has a radial velocity, by observing how the beat frequency shifts when the transmit frequency switches between rising and falling, you can measure that as well.