Unlikely.
I noticed a difference when moving from a Core2Quad to a modern i5, but even that was not a large difference. Heavily overclocked vs stock, I can't even tell a difference in games, so I just set it back to around stock clocks and undervolted, and I'm enjoying the reduced noise.
You're probably going to notice a difference between a Pentium and i3, I'd wager, due to the extra threads and how dumb Windows' scheduler is sometimes, but even that won't be large.
The biggest factor in having a snappy desktop is to have sufficient RAM (4GB minimum, 8GB preferable) and a decent solid state drive. For daily use, I'd take an i3 with SSD + 8GB of RAM over an i7 + 4GB with a conventional spinning hard drive, any day of the week.