Would it be wrong to come for an interview at a another company?
I would say no, as long as it does not interfere with your current tasks or you go on a day off or authorized leave.
Going to interviews while still being employed is quite common actually; you usually don't want to wait until you leave to start looking for other jobs so you minimize your unemployment gap. In other words, you usually want a place to land before you jump (otherwise where are you jumping to?)
How should I explain to them that I'm currently working for a company but they may not hire me for the next few months without sounding like I'm using their company as a backup?
I think it is not necessary for you to explain that in such detail, so I suggest to talk about it only if they ask you about it (like your current work or similar), and if you do keep it simple.
If they ask, I would go for something on the lines of: "I am currently working, but am also looking for other opportunities and I think that your company could be a good fit for me".
Usually, recruiters are more interested in learning about you and your skills (and what you can bring to the company) than about the places you have worked before, so I doubt they will ask many questions about the latter. If you see them deviating, try bringing them back on track with your answers (like the example before) or with questions you have about their company.