Would Q-assign affect Salesforce Assignment Rules if both are running in parallel for different teams?

Q-assign is designed to run within the guidelines set out by Salesforce, the Q-assign scheduler is built to be both highly resilient and efficient.
Q-assign constantly monitors its use of the key Salesforce resources - CPU time, SOQL Queries, etc to ensure that its processes are executed within limits and if needed it will exit gracefully and restart to ensure that the integrity of the processing is never compromised.

If you would like to use Q-assign and Assignment Rules in parallel, you can. Q-assign will only work for the Teams/Markets it is configured for and will not have any impact on other Teams/Markets. We have customers who are using Salesforce Assignment Rules for some use cases and Q-assign for others in parallel, and there are no performance or working issues reported as such.

A few considerations:

To make sure Q-assign and the Assignment Rules work well independently:

Ensure that Q-assign is not configured to process the same records as SF Assignment Rules at the same time (those being assigned and related records in master-details relationships) as this could result in record locking

Please contact us at support@ortooapps.com for any questions.