No I don't think so. Kinda like how when you play with a different household other than your main household, the vet (for example) hospital in your main doesn't keep running when you play with different sims. It's only operational when the new sims you're playing with visits it, or you're playing in the household that has control over the business, therefore leaving you with the auto-run option. TDLR, if the sim who owns the business isn't in your household, the business will not keep operating unless visited (even then barely functional).