Yes, Google will accept a Q&A entry that is both asked and answered by the profile owner. This can be valuable for frequently asked questions or to provide updates for business listings that cannot make posts, like hotels.
According to Google, these are their guidelines for answering Q&As: "Questions and answers are most valuable when they are honest and unbiased. Don’t offer or accept money, products, or services to write questions or answers for a business or to write negative questions or answers about a competitor. If you're a business owner, don't set up stations or kiosks at your place of business just to ask for Q&A written about your place of business. In addition, upvote Q&A in an unbiased manner, rather than a promotional one."
