No, every plan (including Trial) includes unlimited notifications.
However, please note the API rate limit of 800 requests per minute for the Pushy API (60 requests per minute for Trial accounts).
Note: This doesn't mean you are limited to sending just 800 notifications per minute. You can target multiple devices in the same API request which will only count towards 1 request of the 800 requests per minute capacity. You can do this either by specifying multiple device tokens in the same request or sending to a Pub/Sub topic.