Yes!
Transformers work in both directions. You can feed the transformer via the secondary and connect the load to the primary, without causing problems.
There are a few points to consider:
Compensating windings
Many of our transformers have compensating windings. These are additional windings on the secondary which ensure that the transformer delivers its nominal voltage under full load. Without the load the voltage will be several percentage points higher.
If the primary and secondary are swapped over the compensating windings will be on the wrong side of the transformer and the voltage will be lower than anticipated.
These transformers are therefore reversible, but you should take into account that the voltage on the load will be a little lower than anticipated.
Multiple secondaries
Where there are several secondaries account must of course be taken of the capacity of the secondary which is feeding.
Application: reducing the mains supply somewhat
In practice a compensated transformer may be reversed in situations where the mains voltage is higher than is desired. The reversed transformer will reduce the voltage, so that it is closer to the desired value.