Yes, it can. There are many possible solutions, but I think the following ones are the most relevant.

Virtual Machine
This is perhaps the most applicable in your environment. You can download and install an application called a "virtual machine", from e.g. www.virtualbox.org. This application will then emulate an entire computer, so you can safely install Linux without touching any of your "real" hardware.

What you do is basically that you install Linux to a file on your Windows-machine, and run the entire system within a graphical window.

Dual Boot
It is also possible to setup a "dual boot", which means that you pick one of your Windows machines and resize the existing partitions on the harddrive. You can then install Linux to a new partition on the same harddrive; and every time you reboot your machine, you will get to pick whether to start Windows or Linux. Most modern Linux distributions should help you partition your harddrives and setup "dual boot" by default.

Cygwin is the most suitable solution in your situation.
It will help if you can obtain the source code for the program you want to run then you will be able to get a programmer to port any fixes that need to made to the program to run it in a cygwin environment, if any are needed.
The chances are quite high that your program will just "Work."
No constant rebooting or messing around with virtual machines involved.
Cygwin allows you to run Linux binaries from your Windows desktop.

Thanks,
Tony

potential solutions:

Virtual Machines
Dual / multi booting
Live CDs / DVDs / USBs
WUBI (install Linux inside of Windows)
Cygwin (Win32 ports of Linux apps and libraries, not actually Linux)

Multi-booting is probably the most popular solution for home use. However, if you're not comfortable repartitioning your harddrive, I would recommend Ubuntu's WUBI install. Virtual machines are also becoming more popular. If you have the system resources to run VMs, you can try VirtualBox, which is free / open source and is real easy to use.

o.k. they already say all the possibles way to run Linux and Windows, now I'm going to say where and how you can download it.

Lice CD: http://fedoraproject.org/wiki/FedoraLiveCD

Virtual Machine: www.virtualbox.org

Dual Booting: any Linux OS gives you this option at the install time, you just need to have a partition

Virtual Machine: http://www.vmware.com/

may distros has a LiveCD Version. Hope this can help you

For a commercial app in a commercial environment you should dedicate a system to it.

Computers are cheap cheap cheap, vmware only makes sense if there is some other reason to not just get another computer.

If it is important enough to warrant the effort to do it in the first place, then it deserves a proper professional solution, and not an unsupported hack that your successor will never be able to figure out.