The answer is 'yes'
If you want to check your head alignment, the MT side goes in your headstock MT. A lot of test bars are MT3 so if your lathe is MT5 spindle, you need a socket adapter sleeve. With test bar set in place, now you traverse down the bar with DTI in the carriage & it tells how its aligned along the bed axis. This eliminates chucks, collets, gripping discrepencies of cylindrical test bars etc. If the head is rotated any amount, you are cutting a taper. If your lathe allows adjustment, you can tweak it back into position so test bar is parallel to ways.
If your lathe is non-adjustable meaning spindle is bored in the casting, all it can do is indicate that's its misaligned or worn. This is where you get into lathe levelling, which is a misnomer, it really means lathe twisting. Some people believe its better to cut material to confirm head alignment because that's live conditions. It comes under different names & sometimes its explained overly complicated, but I've heard it called the Rolly's Dad's Method. Basically you chuck some stock (no tailstock support), relieve the center section so you have 2 dumbbell shapes on end. Then traverse cut the 2 dumb bells in one pass. Measuring the dumbbell diameter difference tells you the same thing as test bar. Exactly equal diameters means aligned head. Unequal diameters means you are cutting a taper one direction or another. Again, there is no tailstock involved in either of these operations, that comes later. My experience has been cut method works too but subject to more variables involving the material choice, bar length, cutting tools, finish etc. Ideally its a chunk of good quality aluminum because its lower mass (less deflection on the cantilevered end) & cutting finish.
Assuming your headstock is good using either method, now you can do a similar check on your tailstock. MT goes in the TS socket, now you can chuck a DTI & indicate around the cylindrical section sticking out. This then measures tailstock axis in/out and up/down relative to headstock axis. You can do this with a shorter plain arbor too, but the test bar length exaggerates the misalignment. Tailstocks are adjustable, at least in the level plane so you can tweak it back on center. Height is another matter, but it actually is less critical for taper issues.