Technically, no. Maximum magnification is a property of the lens. A 1:1 macro lens will project an image on the focal plane that is 'life size' when focused at the MFD (i.e, a 10mm wide object will be projected as a 10mm wide image), and a macro lens with a 2x extender behind it will project an image that is 2x life size (2:1 magnification, the 10mm object would cover 20mm at the image plane). That's true regardless of the sensor size (or film frame) that happens to be sitting at the focal plane.
But...practically, maybe. It depends on the resolution of the sensor.
For example, consider using the 100L macro lens at 1:1 on a 1D X vs. a 7D - both 18 MP sensors, one FF and one APS-C. Imagine you're taking a picture of a US quarter, which is ~24mm in diameter. On the 1D X, you'll get the entire quarter in the field of view, at 1:1 magnification. On the 7D, you'll cut off Jefferson's neck and the top of his head in the image. But, if you view both images at 100% size on your computer, Jefferson's face will be bigger in the 7D image, because the 18 MP of the 7D's sensor are packed more tightly - higher resolution.
Now, say you repeat the above example, but this time with a 5DII and a 20D. The FoV's will still be the same - larger on the 5DII. But now you're comparing a 21 MP FF sensor with an 8 MP APS-C sensor, and both sensors have approximately the same pixel density. This time, when you view both images at 100% on your computer, Jefferson's head will be the same size in both images, you'll just see more of the field with the FF sensor.
When comparing dSLR's of similar generations, the APS-C sensor usually has a higher pixel density than the FF sensor (that's even true with the D800's 36 MP sensor - an 18 MP APS-C sensor 'upsized' to FF would be 46 MP). Because of that, practically speaking an APS-C sensor will generally deliver a higher apparent magnification than a FF sensor, when comparing contemporaneous bodies.
Hope that clarifies...