Yes and No.
The 15x CMS Site plan is accurate. However, the pricing of $16/month is what it works out to be if you pay for it annually (15 sites x $192 = $2,880 annually, not to mention if you used client billing for profit calculating) otherwise if paid month to month it is $20/month x 15 sites = $300 month x 12 months = $3,600 year.
You could do all that above and not pay for a PRO or Lite Account Plan.
However, if you wanted to add custom code or transfer the projects or keep anything more than 2 un-hosted projects on your dashboard then, YES, you would need to go with at min the Lite Account Plan.
The Lite Account Plan gives you up to 10 un-hosted projects/sites and then the PRO Account Plan gives you unlimited. Which means you can have any number from 1 to 100+ of started projects without having them have hosting added.
As for the form submission quota, that refreshes every month from the time of your billing cycle.
Hope that helps!