Hello Heather,
Yes, it makes sense.
Unfortunately, from the stock screen provided, there is no way to select another team if one person is the lead of more than one team.
However, this can be customized.
One could create a copy of the AddEditWorkOrder screen and in the "Time In/Time Out" section you could add a drop down list.
In the drop down list you can have the different teams, and by selecting that team, you could populate the Employee/Vendor fields.
I hope that helps!