You will not get any noticeable improvement as your games will be GPU bound. Even with the fastest GPU config, I would not recommend upgrading to K as the speed gain would be minimal and probably not even noticeable. I am certain you would be disappointed.
As for overclocking, yes you can overclock a non K to a limited extent. I have experience with overclocking my daughter's i5 2400 so can confirm it is easy and it works. For a non k i7 or i5, intel allows you to overclock it by up to 400MHz. Since the frequency multiplier is locked, you access the speed boost by changing the turbo ratios in the bios. Basically you can bump up each turbo ratio by 4 notches. You might also be able to change the baseclock, but this is more hit and miss. Your maximum baseclock boost is probably only about 1 to 3 percent, after which your system will become unstable.
My experience with the i5 2400 is as follows. It has a stock speed of 3.1 and will turbo up to 3.4. My max overclock therefore increased the max turbo to 3.8. It doesn't get there very often because the higher turbo frequencies are only accessible when running on a single core. It spends most of the time under load at 3.6 or 3.7. I found that my baseclock headroom was minimal so I just left it at 100.
Your i5 2500 has a stock clock of 3.3 and max turbo of 3.7. After overclocking, your chip will run at max 4.1, and spend most of the time under load at 3.9 or 4. You might be able to squeeze an extra 40-120MHz out of it if you adjust the baseclock.
I guarantee that you will find this plenty fast enough. I suspect that overclocking will make only minimal difference to your frame rates, proving that there is no point in upgrading to the K.