Can a transformer be back-fed or used in reverse?

In general, distribution transformers can be reverse connected without de-rating the nameplates KVA capacity. However, this is rarely considered in modern applications due to NEC code changes. Several precautions need to be taken for reverse connection of some smaller transformers. These would include:
Dealing with higher current inrush which can cause nuisance tripping.

HPS transformers under 6kVA three-phase and 3kVA single-phase, there is a “turns ratio compensation” on the low voltage winding. When backfed the turns compensation actually reduces the output voltage.
When a three-phase transformer is reverse connected thus resulting in a Wye-Delta configuration, the neutral terminal must be isolated. This modification may violate the warranty and agency listings such as U.L.

Back-fed transformers increase the installer’s liability since a future user may not realize what is the primary while de-energizing the transformer.

In general HPS suggest that a proper step up transformer which is designed with the low voltage terminals as the primary terminal be used.