Yes you can change from free to paid and vice versa. More conveniently you can schedule prices changes.
Scheduling Price Tier Changes
If you have a Paid Applications contract in effect, iTunes Connect
allows you to schedule price tier changes for your apps over time.
Scheduling is useful for sales and other temporary pricing changes
that have a definite beginning and end date, as well as permanent
pricing changes that have no end. For example, you might offer a
promotional price for a month and then return to the regular price.
To schedule price tier changes, you must have already submitted the
app; the options for price scheduling appear only when you are editing
an already submitted app. For each price tier, you can set an
effective date (the date when the new tier will take effect on the App
Store), and an end date (the date when the tier will no longer be in
effect and will return to the previously set price tier).
You can set up as many price tier changes as you want in advance and
your app will change prices on your effective dates, but no interval
can begin more than a year in the future. Your price tier schedule
will show at all times on the “Rights and Pricing” page for your app.
There you can track when your price changes will occur.