Note that there is a difference between studying grammar and familiarizing yourself with some key concepts of the grammar. I’m in pretty much the same boat, but started on some of the grammar anyway, because I got annoyed at the fact that I was learning verbs but had no idea how to actually use them.
Concepts like ichidan/godan for verbs and whether a noun is a -な adjective have gotten me to pay more attention to some of the other information that is provided when learning vocab. Stuff that I was ignoring up to that point.
My advice is to go ahead and start, albeit not with the intention of memorizing everything right off the bat - note that the reason Tofugu gives for waiting is that once you recognise more words, you’ll have an easier time with context sentences and practice. I do intend to hold off on the serious studying until I’ve gotten a firmer grip on my reading.
