Is it correct to use "serve" in this context?

The word "served" is fine, if you consider that the ministry is providing a service. There are other words that you could use, from the mechanical "to be processed" to the literal "to submit their documents".

I'd move "to be served" closer to "waiting", so the long phrase "at the reception of the ministry" can go at the end

...waiting to be served at the reception of the ministry.