The key thing here is that your BG checks are in progress. That means your application is stuck at criminality or security.
If your application is stuck in criminality, there is a good chance you'll be requested fingerprints.
Applicants mostly get stuck in criminality because their name is a common one and there was a hit/match with a person with a name/DOB who has a criminal record (in RCMP, FBI, Interpol and other police databases). RCMP issues criminality clearance. Criminality clearances are valid for 1 year.
If your application is stuck pending 'Security' checks, then the clearance is pending from CSIS. There is
one case where an applicant was even interviewed directly by CSIS to rule out matches with someone else who might have been deemed a security risk (but this type of interview is very rare). Security checks include deeper look into your background to ensure that you are NOT the person that CSIS is looking for / has some adverse information about. This might also happen if you worked for police / military / intelligence or any kind of law enforcement agencies before (again, this is only one of the possibilities). Security clearances are valid for 4 years.
To find out where your application is stuck, you'll have to order GCMS notes. In GCMS notes, if you see 'Criminality' is 'In Progress', then it is stuck in criminality. However, if you see 'Criminality' set to 'Passed', then we can deduce that it is stuck in security.
Generally, you will NOT receive a test invite unless your BG checks are set to "Completed" (this includes both criminality and security) but I have seen some earlier applicants (from mid - late 2019) receive test invite along with a finger prints request. May be this is done to reduce processing time as they've already been waiting for a long time.