Consumer accounts and Google Apps accounts, can't have the primary email address or alias of any those as an alternative email address. Also Gmail accounts doesn't allow to designate as delegate email access to an account out of the primary domain.

But if you set your Google Apps account to pull the messages from your personal Gmail account, the domain administrator could have access to your personal messages because they are in a mailbox under his control.

References
Sign in to your Google Account with another email address

I'd like to elaborate from my comment above. I would look into using some of the incoming routing options available through the admin console.

Split Delivery

This is where you can deliver to either G Suite or your O365 depending on rules provided.

Dual Delivery

Messages are delivered to both G Suite and O365. I have used this option in the past but with an on-prem exchange server. It worked really well because, in my opinion, Gmail has some of the best spam filters out there and we took advantage of the spam filtering before it was delivered to exchange. Also if Exchange went down we had a backup of external emails.

Have a good read through this G Suite Support Article on Email Routing and Delivery. It'll step you through your setup in the admin console.

Word of Caution

Because you are using an intermediary, you may run into problems with SPF checking. Some mail servers may not like what you are doing and drop the emails. I would look into this question from Server Fault, or this one for some guidance.