It's very possible then. Stock mounts barely hold up to stock power, and a tune will make notably more power. If I were in your shoes I'd do mounts anyway (because they're nearly free power, in the sense that you're not adding to potential reliability issues but making more power because less power is lost in engine movement), at a minimum the powerflex hybrid mount. I briefly touched on it
here with a photo of the tools used to extract the OEM lower dogbone insert, the hybrid puck is cheap and doesn't add a TON of vibration once it settles in. But I would say figure out for sure first if it's tied to vehicle speed, engine speed, relative power request, etc to really nail it down.