Yes it works but if I do that I don’t have h1 tag on single products pages anymore. On my google webmaster tools page “mobile indexing first” setting is on, so it’s important to have h1 tag on mobile version of my web site.
No, I don’t believe it will be bad for SEO, as the titles are the same and one is hidden. However, you may want to do some research on that, as I’m not 100% sure.