[LarryFS]

Probably not.  If the tubes are ok and you do the other standard replacements of old electrolytics, old paper/wax caps, and out of tolerance resistors and the radio works after that, then the oscillator transformer is working.  If you wanted, you could check the resistance readings between pins 1 and 4 - should be approx 7 ohms and between pins 2 and 3 - should be approx 2.6 ohms (see middle and lower portions of Section 4 schematic page for T400 details).