No. Installing the eSIM (loading the profile) does not start the package. The package duration begins only when the phone connects to a supported network abroad with data roaming turned on. So you can install it before your trip with peace of mind, and activate it by turning on data roaming when you reach your destination. (Additional note for iPhone users: in weak Wi-Fi, the "Wi-Fi Assist" feature can rarely use a small amount of cellular data and start the package early — to prevent this, you can turn it off from Settings → Cellular.)