Can something be a Minimum Viable Product if it lacks features that will be necessary for sustainability?

I've heard various definitions of minimum viable product (MVP), but they all focus on a simplified, yet useful, version of the final product.

My team is building a product that currently appeals to a small group of people with special interests. We're hoping that by integrating with other, existing platforms, we'll be able to gain interest from a much larger audience. The latter step is critical to our business plan; the product can't sustain itself unless we can reach the larger audience. It's also the hardest part of the process and will take the most time.

Once we have a prototype without the systems integration, we'll be able to test it with members of our core audience and start iterating on the functionality and UX. However, we'll still need to do more testing with different audiences once the integration features are developed.

Would the version without the integration be considered an MVP? Or, since it lacks functionality necessary for our ultimate survival, would this be a useful test prototype but still short of MVP?

note: this is a simplified description of our product / plan, so I'm not seeking substantive feedback. I'd just like to better understand the concept of MVP.