It depends on the game. For modern AAA games I would look toward 4 cores or at the least a hyper threaded dual core. If the cpu is strictly dual core it may be very limited in games. I'm not sure which games you were looking at where a dual core pentium didn't lose many fps compared to a desktop i5 (actual quad core vs a dual core ht enabled mobile i5). In many cpu intensive games the pentium chokes. It's possible you found a few benchmarks for games that would run on just about any hardware but it doesn't mean a pentium/celeron is suitable.
As an exaggerated example, a pentium/celeron performing fine compared to an i5 while playing solitaire doesn't mean it will keep up with the i5 in bf1. One can't be used to compare to the other. It's not really about which gpu you'll be using, looking to bf1 as an example. The game requires x amount of processing power from the cpu regardless if you're using a 460, 1050 or 1070 gpu. The gpu is responsible for shading and drawing the pictures. Having a lower range graphics card doesn't mean the game itself will require less from the cpu.
The only case where that would happen is if the gpu is underperforming so much that it becomes the limiting factor. For instance a cpu that can only run a given game at 30fps vs 60fps seems bad. If you pair it with a low end gpu that can only run the graphics of the game at 20fps then the cpu no longer becomes the limiting factor. That's a different problem though. It will also depend on what resolution you're playing at, a 1050 can only push so many pixels at a given quality setting. It will perform differently on a 720p resolution than it will 1080p or 1440p.
The easiest way to decide is rather than speculate, wait for a cpu in question to become available and then see how it performs in benchmarks. If the one you're interested in performs well enough then go for it. So far the only tests that seem to be out are from wccftech and I'd take their testing with a grain of salt. They show the pentium g4560 performing similar to a 6th gen i3 in witcher3, makes sense since they're both dual core with ht. They also show it performing similar to an i5k series under ultra hd (1440p) with gtx 980's in sli. It also says 'information in points' whatever that means, games are rated by fps and a variety such as max, average, min, min 1% and frametimes.
http://wccftech.com/intel-pentium-g4560-ultimate-budget-cpu-65-usd/
None of this was mentioned and in previous pentium vs i3 vs i5 tests the results were much different in witcher 3. If the 'points' are fps and they're truly that close I would bet that the game is gpu limited at 1440p with those particular tests and not all the info was included. Drop the resolution to 1080p and consider things like min fps and frametimes and I think it would reveal the 2c/4t pentium/i3 (since they're nearly the same now) suffering from fps drops more than an i5 or i7. One source with partial or obscure details isn't enough to determine much of anything.