Similarly, do safe injection sites encourage drug use? No, because drug use is going to happen regardless of the presence of safe injection sites. It does, however, make it much easier to transition drug addicts into programs that can help them. The data is there.
So bottom line; if you don't like having dirty needles about and open drug use, support safe injection sites. Likewise, if you don't like teenagers getting pregnant or getting STDs, then support access to sex ed and condoms.
Ideally we'd have no-one who becomes addicted to drugs.
But the existence of substance misuse disorders means we will always have addicts, and by definition addicts take drugs even when they know they are being harmed by those drugs. These people are not encouraged by safe injection spaces, because they were always going to be taking drugs.
How are those harms caused? How can we minimise those harms?
Some of those harms are caused by people not being able to access treatment to get off drugs; they cannot access drugs affordably so need to turn to crime to get money for drugs; they have to inject unsafely because safe injection places are not available.
A safe injection space means people are not sharing needles. People are helped to find better injection sites. Any infections can get medical attention before limbs need to be amputated. People can have drugs tested for purity. Ideally we'd be providing medical grade heroin so people aren't injecting contaminated drugs. People can be reminded about evidence-based drug rehabilitation (mostly substitution and therapy. For some reason the US has an over-reliance on abstinence retreats and 12 steps, which has little evidence of effectiveness).
Knowing that there is a safe place to go and treatment for it might reduce some inhibitions about it, but I doubt that many, if any at all, would actually start doing such hard drugs because of places like this.
More likely, if someone is in a position where they would consider doing it in the first place, they would do it anyway.
An adult has the inalienable right to do what they want with their own body.