Well, not normally but certainly anything is possible. If you're going to do that, you will want to have your LLC lease space from you (the homeowner) for some nominal amount....say $1/month for 5 square feet of space. This is no different than your LLC renting/leasing a PO box. If your company gets sued, the claimant cannot sue the Post Office, right? It's the same concept. Just make sure you prepare a Lease agreement and keep it on file. Also you will want to remember to have your LLC actually make the lease payment to you....you know, all T's crossed I's dotted sort of thing.
Now that I've written all of that, I have to say that using your home address as your address for a registered agent is not the best thing to do. Anyone who peruses your State's government website to acquire your company's address (say, a disgruntled customer or stalker for instance) will have your home address. Bad move. Instead, you should serve as your own registered agent, but do so with a PMB mailbox....one offered through MailBoxes, Etc for example. PMB boxes are acceptable since they also have a street address. PO boxes do not. Therein lies the difference.