If an Admin account is removed, will it impact existing backup jobs that is registered to that account?

Yes. The expected behavior is as below

Action

State of Cloud backup data for the affected Agent 
(stays, gets deleted immediately, gets deleted due to retention rules)

Revoke backup plan from the Agent

Stays

Delete backup plan (from end-user account)

Stays

Delete Agent from end-customer account

Stays

Delete end-user account

Backups will be deleted

 

You can re-associate the agents with another account using the following KB below.  If they are part of the same group, backups will be retained.

https://kb.acronis.com/content/55950