You should double check things however.
The transformer itself doesn't care about which phases you use.
The OCPD _might_ care, in that OCPD might only be rated for 240V L-L 120V L-N . In your supply panel you must use a full rated 240V breaker, not a slash rated breaker.
But the biggest question is making sure you understand your service. Depending upon the POCO transformer design, the high leg might be totally balanced with everything else, or might only be intended for 3 phase loads.
-Jon
This^^^
The high leg is a stable Voltage and the transformer as installed only cares about its turns ratio to give you the 120V, so it will do so stably. If you have OCPD in series with that transformer primary or secondary it will only care about the current through it and that should also function dependably.
There are two problems.
If you have 120V already from the regular 120 V secondary windings, why are you adding another transformer to get more 120 V connected in a way that could be non standard and unique across the entire US. The problem is not that it will not work, it probably will effortlessly. The problem is that you could be the only one in the entire US connected this way. You want to know why this implementation was chosen before proceeding.
If you want to say this connection was made to balance the load on the transformer, I would say you are an idiot. And probably should not be wiring anything without standard oversight, someone who knows what they're doing.
A standard red leg transformer is for regular 3 phase loads with usually only a small 120 single phase secondary load. if it's all 120 single phase load at the red leg secondary, the textbook says you can only utilize 57% of the kVA rating of the transformer. Never heard of defeating the textbook on this by loading high leg to neutral with another transformer. That is until you came along.
Back to square 1, what do you want to accomplish. If you want all 120V for single phase loads you should have chosen a Y secondary transformer, or a suitable single phase transformer loaded on the available primary supply Voltage.
The problem you should look at is the original square 1, what do you want to accomplish, and also take a good look at the guy who solved this problem with your unique and non standard solution. He is either brilliant and gifted or accidentally and occasionally lucky.