I have designed a logo in Adobe CS5.1 Illustrator using the ellipse tool to create shapes, filled with colour and then added my type.
The file is saved as
Is it automatically a vector image?
There's no way to know for certain without seeing the actual file.
As a guess, I'd say yes, most likely.
Just because you used Illustrator does not automatically mean everything is vector. If you used, blurs, feathers, glows, drop shadows, placed images, photoshop effects within Illustrator, etc. - none of that is vector.