Running or not, Parallelels and Crossover are two very different technologies. There is no apparent reason why they should interfere with one another.
Crossover is, in simpler terms, merely an interpreter translating Windows instructions to OSX instruction (or Linux instructions). It does require an overhead in resources, but not that much. You are NOT running Windows in any fashion.
Parallels, on the other hand, is a complex technology by which a whole computer has it's hardware recreated in software, allowing a guest operating system to operate "as if" it were on an actual physical machine. Parallels is there to give a fake hard drive, a fake network card, a fake USB controller, a fake video card, etc. All these fake devices must use system resources to be available to the guest operation system. Both OSX and Windows share your CPU and RAM.
This means that once you have booted Windows in parallels, you are running two operating systems at the same time, OSX and Windows, with Parallels itself on top. Running two operating system does require a significant increase in system resources.
In other words, with or without Crossover, the process of virtualization hardware like Parallels does, will always incur a significant cost in system resources. I suspect that your problem lies solely with Parallels/Windows, as that can suck the very life of your system if you are even a little too flush with the base requirements. You might try to reduce the guest OS resources, like less RAM, or less video RAM. If your processor has more than one core, see if you can reduce the number of cores Parallels allows windows to use. That might lighten the load on your computer.