Out of the box, no. When creating a lookup field, you get a dropdown of all objects you can select and the roles you've defined for your Account/Opportunity teams is not available for selection.
The reason for this is that SalesTeamRole is not an object itself. It's a standard picklist that is used on the junction objects between Account/Opportunity and User
In terms of reports, you could get what you want if you're talking about an object related to the teams (Account or Opportunity). You can use the Account with Account Teams report which displays all team members for a given account. Then, you can leverage row-level formulas to match which team member equals the owner of the given account to remove the other team members from the report.
- Create a report using "Account with Account Teams"
- Create a Row-Level formula
IF(ACCOUNT_OWNER_NAME == MEMBER_NAME, "Same", "")
- Add a filter on the report using the row-level formula above so only team members who are the owner of the account show up
- Add Team Role as a column
This won't work with custom objects. With that, you're left with doing custom automation on a custom field (text) to stamp the team role. Depending on your org/context, you could do a scheduled flow/apex or just use apex/record-triggered flows to run on insert and when the owner is updated.