You have the option to "Transfer funds to an existing wallet" (sweep) it to your existing wallet or not, if not "swept" you'll have an option to select that wallet in the 'send' page.
But there's a limitation: you can only import legacy addresses, not SegWit or P2SH.
The consensus here is to keep away from an online wallets anyways, but it's up to you..
That's good information, thank you.
An online wallet is useful if you do not want to carry around a hardware one. The paper wallet / card / OpenDime offer certain special advantages in my case. Having the option of getting BTC out when, for example, overseas, can be useful in my situation.
Also good info on only being able to import legacy addresses. Thanks again.