I have no recent experience with playing live with GR, but for what it's worth:
I used to perform live with GR4 over 10 years ago on a macbook. Never had any issues with serious latency but it came with a pedal board back then which also acted as converter, which made it easier and much cheaper than it would be these days.
Just a note: you're looking at the wrong computer specs. CPU is not that important. I used to run GR4 on a 2.4 Ghz dual-core CPU Macbook with 4GB RAM and it ran great. What's more important is your HDD speed and memory speed. So an SSD is highly recommended for playing live. Also, make sure the laptop is not about to do anything else like scanning for viruses, downloading updates, defrag a hard drive and the like while playing live. You won't be happy if that happens and your hard drive is on 100% capacity. I used to have a separate partition for performing live with nothing but a stripped-down windows with no page file and GR running and nothing else that can interfere with the laptop's performance. Not even an active WiFi/BT adapter. On a desktop all this matters little, but for a laptop it's vital to keep the OS as clean as you can and keep any potential latency at bay.
However, the best way for things like this is to use a macbook. I'm not paid by Apple to advertise their products in any way, but a Mac just does this kind of job 50 times better than windows can with the same specs. And I did try. I already had a windows laptop with the same specs, but it just couldn't do it. It went 100% HDD usage with only 2 effects active. The Mac solved any problem I had or could have had.
I never used amplitube so I'll leave that for others to comment on.
In the end, I did the math on the cost of using a dedicated worthy laptop, the AD/DA conversion hardware and the foot pedal to control it all. When compared to what you can get today in high quality hardware digital modeler/multi-fx, it became sort of a no-brainer. Granted, the laptop-based setup is infinitely flexible and configurable, but IMHO you could just about buy 2 high end multi-fx pedals for the all-in cost of the laptop-based setup. And with hardware, it's ready to go out of the box. No mess, no software installation and associated hassles.JMHO, YMMV.
I can't deny this. There's been a lot of changes over the last 15 years. Back then getting a Macbook (1200E back then) was all I needed (apart from the software and included board, which still works after all this time). But effects are much cheaper and so much better now. And getting an Helix floor would cost less than a macbook, a GR7 license and the required external hardware you'd need otherwise. And you'll lose nothing.
Long story short: In my experience, it can be done live with a good (mac) laptop with an SSD and you'll sound fine with GR. Windows is just horrible for things like this and I don't recommend it unless you're way (and I mean really WAAY) over the requirements. Recording at home should be no problem, even with the windows OS. But I have to agree with @jimfist that an Helix (or similar high end multi-effect) would make it much easier and probably cheaper to get the same results.