If you are:
1. Using FTM 16 - FTM 2011
2. Have a current subscription
The answer is no, you do not have to save to an online tree.
Depending on the version of FTM will determine how you attach to your local PC's FTM.
If you have FTM 2010-2011
Select "Help" on the menu bar
Then select "Training Tutorials"
Once the tutorial has loaded
Select "Web Search" from the TUTORIAL LIST
The Video will walk you through.
For the Pros of having an online tree see the link below
Go to ancestry.com at the home page select "How Ancestry.com works"
Cons
No serious searching and building your tree online if your subscription fails.
Enjoy
RSlack