As previously stated, the DoF of using a 135/2.0 on crop makes the DoF and framing identical to a 216/3.2 lens on FF. However, not only is this the effective focal length and effective aperture as far as DoF and framing are concerned, it is also the effective aperture as far as light gathering goes.
The sensor doesn't do anything magic, other than a FF sensor capturing more of the image circle than a crop camera. Using a FF camera cropped to that central 1.6x area that a crop body sees does the same thing.
By using only a fraction of the available imaging circle, you are using only a fraction of the light coming in through the lens. While a 135L wide open is f2.0, when cropped you've cut out a lot of the imaging circle and therefore a lot of the light coming in through that lens. So, to print this smaller part of the image circle at the same size as an entire FF image circle, you're enlarging the individual pixels more, which means the image and noise are magnified to a greater degree. This effect means that as far as the light gathering goes, a 135L at f2.0 on crop acts just like a 216/3.2 lens would on FF.
To put it in sensor/pixel/amplification terms (and sorry in advance about any long and heated debates this kicks off), if you compare an 18MP 7D and an 18MP 1D X (as they both conveniently have the same number of pixels), the area of each individual photosite/pixel on the 1D X is 2.56 (1.6x horizontal and 1.6x vertical) times bigger than each individual photosite/pixel on the 7D. All things being equal, that equates to each photosite being able to gather 2.56 times as much light on the FF sensor. ISO ratings should be calibrated to be identical - stick an f2.0 lens in front of both sensors with the same shutter speed and the same amount of light, and each camera should produce images of equal brightness. So the amplifiers on the crop sensor are turned up by a factor of 2.56 over and above the FF sensor at any given ISO. Which means ISO 10,000 on the 7D is equal to ISO 25,600 on the 1D X when it comes to amplification, and therefore noise. That difference is about a stop and a third, which the crop of 1.6x is equal to.
And yes, to compare like for like, multiply both focal length and aperture by 1.6x to work out what a FF equivalent would be. These compact cameras like the FZ200 with its 4.5-108/2.8 lens winds me up by proudly having 'f2.8 25-600mm' written in big letters on the side of the lens. If they quote the focal length in FF equivalent, the aperture should be written like that too. Its the equivalent of 'f15.7 25-600mm', and no more...