Overclocking will offer a significant improvement in more CPU bound games, eg. a lot of the open world stuff that has come out lately like GTA V, the last two Assassin's Creed installments, online shooters with large player counts like Battlefield 4. For games that aren't all that CPU heavy, you wouldn't see much of an improvement.
If you have a motherboard that can't overclock, then you may want to consider simply saving up some more money and doing a full platform upgrade to something more modern. It doesn't have to be done immediately, and you should be able to ride out a 2500k at stock for another year or two without much trouble. The small incremental upgrades Intel has made in the past few years have started to add up to the point where current CPUs do have a noticeable advantage over the old Sandy Bridge chips. You'd also get more chipset features like more 6Gbps SATA connectivity, more USB 3.0, USB 3.1 support, M.2 and SATA Express for high performance SSDs and PCI-E 3.0 support, which will probably start to become beneficial soon with advancements on the GPUs.
If not, good luck finding an LGA 1155 motherboard, there aren't many new ones left out there, and you may have to look to the used market to find a decent one.