This varies based on your store's Mechanic configuration. As a development platform, it's possible for a developer to integrate parts of Mechanic with an online store theme. This is always a manual step, however, performed by a developer – a Mechanic account does not intrinsically require any theme modifications, and does not require any preparation when switching themes.
In most cases, switching theme does not require any coordination with Mechanic. For confirmation on your specific case, work with whoever configured your Mechanic tasks.