Hi Martin,
I must say in advance - I am not an EASA Staff member and new to ATOs, but please allow me to share what I've found.
And please double check my answer.

I think the answer to your question is:
For the majority of the course, yes. You can use the SR20 with a non-retractable gear for the flying training.
However, (EU) 1178/2011, Part-FCL, Appendix 3 sets out the training courses for CPL and ATPL.
Section E describes the modular CPL in which the paragraph Flying Training, Point 11 lays down:

"At least 5 hours of the flight instruction shall be carried out in an aeroplane certificated for the carriage of at least 4 persons and have a variable pitch propeller and retractable landing gear."

Again, please double check on my answer and maybe there is an EASA staff who can confirm my statement.

Best
Keno

Thank you, Keno, for answering the question. Our experts agree with you. If someone needs advice like this, I suggest they contact NAA or ATO, who can also help.