Very unlikely. NIH only allows Cost Share on Awards where it is stated in the Program Announcement that Cost Share is required (very rare), or will be a factor in selecting the Award recipients.
So unless the Program Announcement states that Cost Share is a factor, Cost Share should not be included in any NIH Award.
For Training Grants, funds are limited and are to cover the costs of supporting the Trainee. The salary of the PI is an allowable cost on a T32 Training Grant but, typically, there are insufficient funds to cover PI or other staff effort on the Award. The PI may choose to have their effort paid from non-sponsored funds. While PI and other staff will expend effort on the Award, and that effort paid from non-sponsored funds, that effort does not need to be recorded as a Cost Share commitment unless the Program Announcement specifically states that Cost Share will be a factor in Award selection. To the best of GCA’s knowledge, an NIH Training Grant Program Announcement has not included Cost Share as a factor.