As the title states. I'm building a budget pc. I'm concered if it will do a hard bottleneck or not.
It's a perfect match imo. We sometimes get a bit too focused on the balance. In this case, yes the 1060 is slightly better than the G4560 but unless the G4560 is the last CPU you will ever buy the 1060 is a perfect pairing. The 1060 will allow other upgrades to happen and can save money in the long run. It's usually better for the GFX card to slightly outpace the CPU.