Yes but the KVA is reduced 1/3 and some manufacturers have guidance on this when it is a dry type. Some specify a 5% kVA for the center tap for the unbalance or something like that.
Seems to me that the 5% limit on the center tap would not apply for the condition that all of the secondary loading is single phase C-N-A.
The reason for the 5% limit on the center tap is the effect of circulating current in the delta secondary: for any given load currents and coil impedances, KVL around the delta loop requires that the voltages sum to 0, which determines the circulating current necessary to make that happen.
Consider the best case that the primary voltages are all balanced (if not, there will be a no-load circulating current in the secondary) and that the coil impedances are balanced; i.e if the impedance C-N is Z, then N-A is also impedance Z, and A-B and B-C are impedance 2Z. Z can also incorporate the effect any of any (balanced) primary impedance.
Then for the case of a secondary load current +I that is only supplied C-N, no other loads, the circulating current will be -I/6. So the net currents will be -I/6 in A-B, B-C, and N-A, and 5I/6 in C-N (all in phase). The voltage change around the loop is - 2Z * I/6 - 2Z * I/6 +Z * 5I/6 - Z * I/6 = 0.
So for a single phase only loading the circulating current actually decreases the maximum current in the coils, and if all these balance assumptions hold, the available kVA would actually be more than 1/3 of the transformer kVA.
But suppose we have the unbalanced C-N-A loading along with full loading A-B and B-C. E.g. a resistance R applied A-B, another resistance R applied B-C, and a resistance R/2 applied N-A, where R is chosen so the load current I equals the transformer rated current. This is the loading case of a fully balanced 3 phase load (which would have no circulating current) minus the first case above.
Now the circulating current will be I/6, the negative of the circulating current in the first case. This won't overload the A-B or B-C coils, as their currents are 120 or 240 degrees out of phase with I, so the magnitude of the vector sum is not increased. But this circulating current of I/6 is in phase with the load current I in the N-A coil, and the total current in the N-A coil will be 7I/6, an overload.
This phenomenon is the reason, as I understand it, for the 5% limit on the center tap of 240V/120V delta secondary, and as we can see it only arises with 3 phase loading.
Cheers, Wayne