Yes, although the punishment shouldn't be the same as for crimes like eg. theft.

As for why, two main categories of reasons. First, for the good of the person themselves. By making it illegal, the state then has the authority to compel some sort of action. For a first 'offence' this could simply be sleeping it off in the 'drunk tank' (or in a hospital bed if necessary). For repeat offences, an escalating scale of compulsory treatment. Basically if a person is regularly passing out in gutters, it's likely only a matter of time before they kill themselves, so being nudged, then coerced, then ultimately compelled into treatment would likely benefit them. Of course, this relies on avenues for treatment rather than simple punishment being available.

The other reason is for the rest of society. People do not want to walk down streets where people are passed out in gutters. They will either feel compelled to try to help - which can be, or at least feel, risky, given that intoxicated and/or mentally ill people can be unpredictable - or they may feel badly for not doing anything. Regardless, if it's a regular thing, it will encourage people to avoid the area where they're likely to encounter such things. That will impact local businesses, residences, etc., leading to an overall decline of environment and services for everyone.