It appears from your current score that you have pretty much removed all derogs, as having a score in the 700 range with only one open account indicates a pretty clean payment history.
With that assumption, my question would be... how soon are you planning to app for the mortgage?
App for an installment loan now would most likely result in little FICO gain, as it would involve a new inq and would add a new account with zero age to your AAoA calc.
While it might have an offset with an improvement in credit mix, it most likely will not have significant FICO impact one way or the other.
Perhaps more significantly, a lot would depend, in my opinion, on other non-FICO factors that will enter into a mortgage app process, such as total income, assets, and debt.
Some mortgage lendors, for example, dont like to see acquistion of other new debt just prior to the mortgage app pocess.
If I were in your situation, I would most likely contact the prospective mortgage lendor and ask the same question of them, since a mortgage app process involves quite a bit more than just a three digit FICO score, and only they can tell you how they would view it. They may like it, or advise against it.
