How a golf competition is run is entirely up to the organising committee. That being said, your real question should be whether combining handicaps calculated by two different systems in the same competition would be equitable and lead to a fair result. I don't have an answer to that.
I've no idea what System 36 is, but a competition's organisers get to decide what handicaps they intend to use (if any). There are no rules that limit their imagination! It's your choice to enter the competition or not, based on their terms.
Providing a player is only required to record their gross score on the card I see nothing wrong with what a committee then does with that score.
If a player does not have a WHS handicap index and is playing in it I assume that this is some sort of unofficial comp anyway.
When it comes to 'unofficial' comps I have played in lots where several of the players did not have official handicaps although I used to think it very unfair that most were given the maximum handicap (then 38).