The CRA number is of less importance in the direct to PR category. However, if they are doing gaining experience, they would need to do the CRA number because the offer of employment form requires it. Most legitimate businesses will have the CRA number. However, there is the possibility of an independent contractor scenario which generates a T4A. If the HSWP/HCCP candidate has been filing their own taxes from gross income received in cash, they won't have a T4 but they will have an NOA and T4A to show as proof of experience along with an experience letter from the employer.
While there isn't something called a caregiver payroll account, if the person has an LMIA-based work permit or a PGWP, they are legitimately working in Canada. How the payroll is settled has so many unconventional possibilities, though. Some people get cheques straight from the long term care insurance of the "patient" or they get government cheques directly sent to them as independent contractors for those "patients" who get government subsidy for their PSWs (HSWs). This is, of course, less common in HCCP that doesn't involve disabled children.