Is it acceptable/worth it to cold email an employer I’d like to work for?

I’m on holiday in Japan at the moment, and yesterday I visited an art gallery whose approach to curation and exhibition really resonated with me. I was going to send them an email saying how much I enjoyed the gallery anyway, but the more I think about the more I wonder if it would be acceptable and worth it to ask if they’re currently hiring.

I will soon graduate from an Australian Master’s degree majoring in Art Curatorship, and have written my thesis on some of the artists and genres that the gallery exhibits – so I suppose I have some experience that may be of value to them. I speak very little Japanese but would be willing to learn at my own expense (at a language school/class or similar).

Living in Japan would be interesting, but I feel that working for this specific gallery – even as an intern or on a short contract or similar – would be incredible for me. Has anyone had any luck cold-emailing potential employers? Is this ‘done’ in Japan or would it come off as odd?