Hello Ash Ish!
That should be possible, as long as the PSU can power both cards, and the motherboard has two PCI-express slots.
From personal experience, I got two monitors linked to one GTX 650, I decided to fill the second slot with my old ATI Radeon HD 4650. Each GPU was connected to one monitor and both worked fine. (Didn't try to install AMD drivers though). I could drag stuff from one to the other monitor seamlessly, gaming would probably suck on the monitor connected to the old gpu though.
The main problem now is, if you only own one monitor, you cannot have two GPU's on the same screen working at the same time, that's what SLI/Crossfire is for.
For example, if the monitor has 2 inputs (VGA, HDMI, DVI), you could connect one GPU with a HDMI cable to the monitor and the other GPU with a VGA, DVI cable to the monitor. In the end, the monitor is connected to two GPU's by two wires. With this said, when you want to game, switch to HDMI (connected to gaming GPU), if you feel like designing/modelling, switch to VGA or DVI (workstation GPU).
Do you understand? Take this scheme with a grain of salt though, I have no experience on how will two different drivers behave in an environment like this.
Or you could just get a high end graphics card that can do both tasks.