They help, but plurarity is by far a much bigger factor. And the liberal party will eventually be full citizenship, around 1890 or so.
Basically, the factors that draw immigrants are being civilized, plurality, continent (America, Asia, Africa, Europe in order of preference, although this matters more for where the immigrants actually go if they choose to move to your country), being the USA tag, citizenship and religious policy of your ruling party, government type, matching state religion, social reforms, not being in debt, and RGO/factory types/open slots, pretty much in that order of importantance. They are all relative to each other though; having a slavery party means your plurality must be significantly higher than the guy with full citizenship to be able to compete.