The Mishna L'melech (Hilchos Terumos 7:1) questions what the halacha would be for a tamei kohen who eats teruma that is only tamei m'drabonon. Is the kohein chayav misah since on a Torah level the teruma was still tahor and he violated it, or is the chiyuv misah reserved for eatable teruma and since this teruma was tamei m'rabonon and not eatable, he wouldn't receive misah bidei shamayim? The Mishneh L'melech proves his points from a completely different context where a similar question can be asked. The Rambam (Hilchos geneiva 2:8) writes tahat if one would steal and shecht an animal in a way where the shechita would invalidate it only d'rabonon (such as chulin in the courtyard of the beis hamikdash), he is obligated to pay the 4 or 5 payment, since m'doraysa it was a valid shechita. Although the animal is practically inedible, since it is technically permitted m'doraysa, there is a chiyuv 4 or 5. Here too, since the teruma is tahor on a Torah level, the tamei kohen would be chayev.
It seems to me that this can be proven from a more localized din. Tosafos 83b raises a question, how can you have tahor teruma that is still tahor at the time it is being eaten and wouldn't become tamei by the kohen's touching it? Tosafos offers some scenarios such as not being huch'shar (susceptible) to tu'mah. Then Tosafos answers that it would depend on whether the Tuma on the kohen's body preceded the tu'mah on the teruma, or the reverse. Meaning, Tosafos holds that even if the teruma were tamei d'oraysa, the kohen would be chayev misah for eating it if his tu'mah preceded the tu'mah on the teruma. From here we learn that we don't look at whether the teruma is practically eatable or not. Rather, we look at the technical relationship that the kohen has to the teruma. Since the tu'mas ha'guf of the kohen created an issur on him to eat the teruma prior to the teruma itself becoming ta'mei, we consider him to be actively mechalel (violating) the teruma when he eats it (even though when he actually ate it, it was already tamei). Therefore, this should certainly be true if the teruma was only ta'mei m'drabonon. Meaning, even though the teruma cannot practically be eaten, the tu'mah d'oraysa status of the kohen (even if it comes after the tu'mah d'rabonon of the teruma) should create a technical prohibition to forbid him from eating the teruma and he should be chayev mi'sah.