My current kernel (whatever is built into stock Froyo 2.2 ROM for Verizon Motorola Droid X) does NOT support swap memory.
Does CyanogenMod 7.2 kernel support swap memory? Does that depend on device-specific build?
The cyanogenmod team feels that swap doesn't serve it's purpose on an Android device:
You can read all about it at the Swap and Compcache - CyanogenMod Wiki!
To answer you question directly, by default the swap and Compcache schemes are disabled, but if you still feel the need to use them, above link provides you with a how-to.
So, yes, the CyanogenMod 7.2 supports swap and its usage needs to be activated.
The swap and Compcache schemes usage depends on the device and its support for it.
As a side note, the CyanogenMod 7.x is Gingerbread-based not Froyo, as can be read here:
No. Kernel support is missing. You need to replace the kernel.
Longer answer - check answer from Zuul.