First of all, to an extent, Canada already has a partial universal...which is pretty much a paradox, but you get the point. Would it reduce inequality or not? Would it be a good thing for the low-income earners? It all depends on the parameters of the measure. It can make a lot of people worse off. It would be a lot of money going into a social program that could go instead into public services or more specific transfers. I'm not talking about a really narrow means-tested program. If it were universal, you'd be putting a lot of money on the table. Right now, seniors get $16,000 per year in transfers. If you don't want to have anybody worse off, you have to give everybody $16,000, or else you adapt it a little bit to the needs of the people.
To answer your question, it all depends on the parameters. That is a question with no easy answer.