Then digital tape would sound like analog tape, so no.
But you are partly correct. Analog tape sounds like analog tape largely because of the medium. The non-linearities of tape is a significant part of it's sound, including the famous tape compression.
Magnetic tape is not an easy format to record on. Early recordings sounded like crap, and was not usable for anything but voice recordings. Not until two guys at AEG, by mistake, in 1941 notice that overlaying a high-frequencey signal improves the sound significantly does it gets usable for music, and even then it wasn't very good. It still needs a whole bunch of filtering mechanisms to make the frequency response anything even remotely like flat.
Here are two enlightening pages on that topic:
http://www.endino.com/graphs/
http://www.digitalprosound.com/Htm/TechStuff/2000/Aug/AnalogTape2.htm
Recording to tape, even high-end tape, will impose a certain sound on whatever you record.
"To me, analog is unpredictable; it does that funny thing to the bottom end. You work really hard on the bottom to get it exactly right, and then you play it back on your analog tape, and it's like, 'Oh, what happened there?' The storage medium is making decisions about what the bottom end should sound like." - Bob Clearmountain
High end digital does not do this. Low end will probably fuck things up, just as low end analog will, but high-end digital is WAY more accurate than analog tape is. And this, to me, is the power of analog: It will make things sound *good* and *coherent* because it imposes it's sound onto whatever you record. Digital just plays it back as you record it.