Should a soldier with sufficient leave (45 days) work through a leave cycle, despite having no deployment training? Should I report him/her?

What are you going to report, that some mandatory training has not been completed? See AR 600-8-10 Leave and Passes chap 2, sec 1, Policy for Leave. While there are valid reasons to deny leave (i.e. insufficient accrual, treatment for infectious disease, mission requirement, etc) this doesn't seem to one of them. If you are that service member’s supervisor, Command is not going to ask the individual why he/she has not done the training, they will ask you why that was allowed to happen.

This may have a negative affect on training percentages, but that is not on the individual taking leave. The commander will have to answer for all needs training bullets.

If the Soldier wants to take leave and is caught up absolutely. But he can still save it and if he takes leave the next block leave period he should continue to remain under the use/lose so it really up to the Soldier and your chain of command.