It’s difficult for anyone to say unequivocally whether doing any particular thing will improve search ranking (except for some obvious measures like moving content from behind a pay wall) For one, it depends on the search engine. You are probably focused on Google. There’s only a few Google engineers who can accurately answer your question, and they are not talking. The rest of us are guessing based on mostly anecdotal evidence. And what we decided works last month may not apply next month.
I personally don’t think tags will help, but it’s a possibility. Like nearly everyone else, I don’t know how Google ranks content. The main thing is to be sure there are links from other pages to the content you want indexed. Use an XML sitemap and be sure the links are on there as well. Be sure the Google bot can access your content. Use the “Fetch as Google” tool of Google Search Console to be sure the bot has no trouble. If you have not used GSC, you should start. The bot can sometimes have difficulty accessing individual gallery images because of how the gallery is implemented. I’m not familiar with this plugin, so I could not say if this might be an issue.
It’s probably a good idea for images to be accompanied by descriptive text, IMO. This is where tags might help. Not as tags per se, but merely as additional textual information. Unless your previous URLs correlate with the new WP URLs, you should setup .htaccess 301 redirects from old to new. My understanding is the new page will then inherit at least part the previous page’s page rank. Even if it didn’t, you should still setup redirects for the benefit of your visitors. Redirects probably also increase the chances of the new content being indexed.
Finally, realize that it can take a good amount of time before Google gets around to indexing new pages.