Can I define a flex position comprised of positions that aren't in the starting requirements?

Yes, but there are a few steps involved.

1. Go to League >> Settings >> Edit Roster Requirements >> Custom and click New Position. Add the position you want to flex with 0 start value, a 0 min value and any max value greater than 1. Click OK.
2. Now add a New Flex and select the positions you want to flex with the new position you just added and click OK.
3. Click the save link on the top of the page.