Can we rank in cities where we have no address?
In organic results, yes, with genuine service-area content. Map pack visibility is heavily tied to physical proximity, and we won't pretend otherwise.
Local SEO
For most local businesses, the three map results matter more than everything below them combined.

Someone searching a service near them is close to buying. They rarely scroll far. Appearing in the map pack, with strong reviews and a page that answers immediately, is often the entire game.
Local SEO is the work that gets you there: profile accuracy, proximity relevance, review velocity, and a website that reinforces all of it.
Local rankings come down to how close you are to the searcher, how well-known and well-reviewed you are, and how clearly your content matches the search. You can't move your building, but the other two are entirely workable.
Prominence is built through reviews, mentions and consistency. Relevance is built through specific pages about specific services in specific places.
Questions
In organic results, yes, with genuine service-area content. Map pack visibility is heavily tied to physical proximity, and we won't pretend otherwise.
More than the competitors you're trying to outrank, arriving steadily rather than in suspicious bursts.
Tell us your city and service and we'll look at what the competition actually looks like.