I think your suspicion may well be correct in terms of how the proposal will develop. At present the referendum questions reads "Soll jeder Mensch in diesem Land die finanzielle Grundlage zum Leben bedingungslos erhalten?" (roughly, Should every person in this country be given the financial basis to live decently?), but Switzerland has a fairly strong anti-immigrant lobby, and I would expect to see that interpreted to exclude non-national residents.

Beyond the increase in rents, I would also expect a consequence to be for the tax regime to become less progressive (perhaps a flat tax rate) and more rigorously enforced. This might add up to making Switzerland an unattractive country for people to work who do not intend to take citizenship.