I'd recommend against it. It'll create confusion about who's really in charge and distinct risk that the owner (intentionally or unintentionally) undermines decisions you need to make.

I've invested in 25 search fund deals in the last 5 years and had my own deal back inredactedseller did not stay on in that one). I have seen the Seller stay on in roughly 1/3 of the deals. In most cases, the Seller staying on has been a big positive primarily in generating sales or helping promote the company in the industry to help source add-on acquisitions. The key is obviously having 100% alignment with the Seller on their role and being very clear with employees post-close on that as well.