Yes. When you upgrade or downgrade a plan, the billing date will be restarted based on the time of this change.
Customers who are upgrading a plan from an active subscription will receive a proration discount, based on the unused portion of their previous plan.
Customers who purchased a lifetime plan will be eligible for a proration discount only if they upgrade their plan within a week (7 days) from the time of purchase.
Downgrading will remove features. You therefore may want to wait until your subscription gets near the end of the paid period.
Please find the details with examples on Freemius’ page.