H1 tags are pretty important as they are meant to be the header of what the entire pages is about. Every page should have 1 and only 1 H1 tag and should definitely contain your most targeted keyword.
It's OK to have multiple H2, H3, H4 tags though. Although they don't count as much as an H1 does, it's still important to include your keywords in these tags when applicable too. Make sure that you're not "keyword stuffing" either.
So to answer your question, yes, if you don't have H1 tags on a page, and then add them in with the appropriate keywords, they will def help your on page optimization!
Hope that helps!