Sure as long as there isn't any STR or sublease restrictions in your rental contract and your city/county allows it.

Any other restrictions?

Distributions are handled the same way, and subject to the same restrictions, as a regular 401k. 

So that would ultimately restrict my search to investors selling off rental properties?

@Jordan Deeney @Brian Ellis @Carl Dowdy this topic is quite involved and I hope to help a little with this subject.If you are using a Fannie/Freddie loan with your refinance step they are good loans for their rates and terms but they do have restriction on how much cash you can take out in the first 6 months of the property. 

@Eddie Pfeifer The changes that went into effect for 2018 now restrict 1031 exchanges to investment real estate only. 

The City of San Jose has restrictions on living out of your car and how long you can park your car in any one place on the street.

Maybe take some shots of cat crap every visit "to document noncompliance with lease restrictions"?

Are there any restrictions against doing something like this?

Purchase: For a purchase money transaction, the LTV is determined by dividing the loan amount by the lesser of the “as completed” appraised value of the property or the sum of the purchase price of the property and the total rehabilitation costs.Refinance Transactions: For a refinance transaction, the LTV is determined by dividing the original loan amount by the “as completed” appraised value of the property.Eligible Renovation: There are no required improvements or restrictions on the types of repairs allowed.