No you would have to apply to the competent authority for the issue of the SFI. The TRI automatically fulfils all the requirements so they should just issue it no problem.
I have know of TREs that have lost their medical and applied to the authority who just issued a SFI and SFE cert without question.
TRI may be valid without a class 1 but you have to ask your CA. I know the IAA tend to allow some instructional duties on a case by case basis.