I think it would be a great idea! I can't think of any downside, except of course the amount of work, and I have absolutely no technical ability to assist with that. It makes sense that you're looking for a consensus among the community before taking that step.
In 2015, Cooking:SE Meta had a Community Promotion Ads campaign. Gardening:SE created an ad and submitted it to that campaign. It was subsequently posted on Cooking's main site. I believe other sites, some of which were small or new, ran ads there too.
I don't know how often it ran or for how long. I also don't know how successful it was in driving traffic to the site. I'm sure there are statistics that can be accessed by people who know how to find those things!
I look forward to seeing what other people think about running our own ad.
NOTE: The rules for size and other things have been changed since that campaign on the Cooking site. I'm leaving the link as an example of what some of the submitted ads looked like at that time. Please see Charlie Brumbaugh's meta post, Suggesting Community Promotion Ads, for the current instructions and requirements, and a more relevant link.