I'm sure that it being listed as both in the database is a oversight. It is a tetraploid and no you cannot tell which is which by its roots. Actually you really can't tell which is which just by looking at any of it physical characteristics. If anything sets them apart, IMHO, is the blooms and that's just the toothy ones and the chicken fat ruffled ones. I don't think there are any dips with teeth or the really ruffled edges. But the most sure way is to look at the pollen.
I had someone ask me in my garden if you could tell a dip from a tet by its foliage (they were telling people that is how you could tell them apart) so I took them to 2 of my beds that are side by side and ask them if they could tell which plants were dips and which were tets and they could not tell me which was which. One bed was nothing but dips and the bed across from it was nothing but tets.
You asked "Can a diploid and tetraploid be crossed?"
Yes and no. You can cross a dip onto a tet and it may make a seed pod but it will eventually abort. If you have a dip that may have been treated to try and convert it to a tet ( but didn't succeed) it may still have a little bit of tet in it (making it a chimera???) and actually take on another tet; I have several seedlings that have a tet pod parent and a dip pollen parents but I know the dip was one that had been treated to try and convert but it was not fully converted or reverted back. It was an accident that this happen the first time as Kim had accidently planted a tet in her dip section and kept putting dip pollen on it and we had it actually take so then I started putting the pollen on a very fertile tet I have to see if I could get it to take and I have about 6 seedlings out of that.