Will changing email associated to iCloud change my iCloud email address as well?

A Gmail address can be used with an Apple Account, but does not have iCloud storage or related iCloud features.

If you change the Gmail address, you must also (separately) change the email address associated with the Apple Account.

Apple isn’t tied into Gmail details.

Before shuffling email addresses around, I would set up rescue email address to some other email address not involved in the shuffle, and would set a recovery telephone number, for the Apple Account. This to provide reliable paths back into the Apple Account, should something get snarled at Google or at Apple in the shuffle.

• Change your Apple Account primary email address - Apple Support (change email address)
• About your Apple Account email addresses - Apple Support (rescue)
• Add or remove trusted phone numbers on Mac - Apple Support (trusted contact)

No, it will not change it. You couldn't change the iCloud one once created even if you wanted to. So your iCloud mail address would remain hi@iCloud.com. If you do not like that, use an iCloud alias instead. Add and manage email aliases for iCloud Mail on iCloud.com - Apple Support - "An email alias is an email address that conceals your actual email address from a recipient. An alias can help you manage the email you receive, and monitor the sources of unwanted messages. You can both send and receive email from an email alias using Mail on iCloud.com.

What’s your general goal here? What problem are you trying to solve?

An Apple Account with its mail at Apple iCloud has that email address, and can have alias email address entries.

If you change the AppleAccount to a different iCloud address, or to an email address on an email service elsewhere, you will no longer have the original email address.