Yes, this is possible. The best way to do it would be to print the direct track outs from the 4-track into your DAW interface and software (assuming you have a 4+ channel interface, that is...otherwise if you only have a 2-channel interface, you'll have to print in two tracks at a time and line the tracks up manually in your DAW to get the timing right).
It's actually fairly common for music to be tracked to analog tape then print the tracks into a DAW for editing/processing/and/or mixing these days, it's a kind of compromise between the "analog tape sound" and the "convenience" or "flexibility" of digital production.