It depends.
By default, Primary Owner, Owners, Admins and Full Members are allowed to install any applications for Slack. However, a workspace admin or owner may limit installations to pre-approved apps. If Backupery for Slack is not in the list, then you’ll see the following message while installing the app:
It means Backupery for Slack is not on the list of approved apps. At the moment of writing, we are not aware of any notifications being sent to admins, owners, or any other members about unauthorized installation attempts. To request the addition just click “message one of your admins” or contact them directly asking to add the application to the pre-approved apps list. You may send the following Slack App Directory link so the admins could approve the app faster: https://slack.com/apps/A1R9DMFS7-backupery-for-slack
Read more on how to manage apps for a workspace: https://get.slack.help/hc/en-us/articles/222386767-Manage-apps-for-your-workspace
How to add an application to Approved Apps if you are an admin or owner: https://get.slack.help/hc/en-us/articles/222386767-Manage-apps-for-your-workspace#create-a-list-of-approved-apps