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An aircraft can lock onto the location of a VOR and we can see the QDM (magnetic bearing to the station) to the VOR. If this is the case, do we still need to know the true track of that route? And if so, why?
By extension, if we essentially have all we need to get to the VOR in the aircraft, why do we need to know about QTE (true bearing from the station)?
NB: I have no experience in flying a navigation flight
The short answer is no, you don't need the true bearing to the station if you have magnetic bearing. Presuming of course that your airplane has a magnetic compass to fly that bearing, there is simply no reason to convert to true.
You don't get either and you don't need it.
The VOR signal gives you a radial to the station. This is normally referenced to magnetic north, because that's what you have on board¹, but it might have been last aligned twenty years ago and so might be a couple of degrees off as the magnetic declination slowly changes over time.
It does not matter what it is anyway. The instrument works so that you select the desired radial and it shows you how far (in degrees) you are to the left or right. You align yourself roughly in reference to the magnetic compass and then you steer right if the needle is on the right or moving to the right too fast and steer left if the needle is on the left or moving left too fast, until you manage to centre the needle.
At that point your heading is something that depends on wind and the misalignment of the VOR. But you know you are following the radial that defines whatever airway or procedure you are flying and that's what you needed.
Note that when the VOR is re-aligned, all the charted procedures have to be updated to the new radials, so they don't want to do it that often. Having the radials off by a degree or two is not a problem, because the heading does not match the radial due to wind in practice anyway and updating all the maps is a lot of work.
¹ A gyrocompass is only self-aligning when moving slowly, so while they can be used on ships, on aircraft the heading indicator is always slaved to the magnetic compass. You can now get true track from GPS, but then you don't really need VOR anyway. VORs exist for aircraft that don't have GPS or their GPS failed.
The radials extending from the VOR are normally based on local magnetic variation (the compass rose around the VOR on the chart is angled off true by the amount of local variation so that the 360 deg Radial is pointing to the magnetic pole). The VOR gives no bearing information relative to the airplane; it only tells you that you are somewhere along, or to one side of, a selected radial extending from the VOR, regardless of which direction the airplane is pointed. But since the radial represents a magnetic track, you fly magnetic headings to orient yourself and and stay on the radial you're on as you fly toward or away from the VOR.
Except.... if you are in the Canadian Arctic, in an area called the Northern Domestic Airspace (the Northwest Territories and Nunavut more or less), the compass is useless because the magnetic pole is right in the middle of it, and everything, airway tracks, runways, VOR compass roses (the few that are up there), are oriented to true. In that case you fly true headings and tracks, and if you are tracking to the Cambridge Bay VOR, it's radials are also true, and heading information has to come from a directional gyro that is aligned to true heading, and your compass becomes a nice instrument panel ornament.
You do not need the true bearing to the station in order to navigate to it. However, if you don't have a GPS or other NAV equipment on board, you need some way to estimate your groundspeed, and knowing the true bearing can help you do that. Winds aloft forecasts are given with reference to true north, so if you know your own track relative to true north and your wind correction angle, you can deduce your groundspeed with it. You can check this against your resulting calculation of time to the VOR station to confirm it. All of this is important so that you don't run out of fuel. Luckily, having a GPS on board, or even a DME, or even another VOR radio, will allow you to do redundant groundspeed calculations without all the math or winds aloft tables.
