Will I able to play game with Intel Pentium G4560 LGA 1151 CPU, ASUS ROG Radeon RX 470 Strix and 16gb ram while streaming?

What game(s)?

Gtav no of bf1 is part of the bf series no, rest I'm not familiar enough to know I'd suggest at least an i5 to try and stream. If I could wait a month to build I'd wait and see how much a 4c/8t ryzen CPU will cost in early march

Don't know if you intend to watch streams while playing or plan to stream yourself, but I'll assume the later.

Of the games you listed I will give some opinions on how it might run on that system:

GTA5: Most likely not while streaming, There is even a difference between an i5 and i7 while not streaming the content.
outlast: don't know
fallout4: Most likely not, my i5 is clearly loaded when I play, and I don't stream my games.
csgo: Should run fine on your rig, but streaming most likely will be to taxing while gaming.
Hitman series: The older titles should run fine, the newest one not so much.
left 4 dead 1 and 2: Should run great and streaming could be pretty much possible.
Half life series: same as with L4D, same engine, released around the same time.
Call of duty series: I think up to MW3 all games should run pretty much flawless, including streaming. After that the requirements have greatly increased.
battle field series: BF3 should run fine, BF4 maybe aswell, BF1 could have problems even without streaming.
Dying light: don't know, have no experience with it.
watch dogs: The first game should run fine, the 2nd should have issues
sniper elite series: The first two games should be fine, the 3rd maybe.
Batman series: the forst 2-3 games should run flawlessly, the 4th might have issues, depending on the current state of the PC port.
sniper ghost series: same as with sniper elite. first 2 games should be fine.
Dead space series: the first game should definately run flawlessly, can't say much about the others.
crysis series: All games should run atleast for gaming alone, but the 2nd and especially the 3rd installment might get trouble with streaming.
Max payne series: all of them should be fine.
walking dead series by telltale games: should stream fine.
batman by telltale games: same as with walking dead.
Tom Clancy's Rainbow Six Siege: Don't know, but you might get some trouble
some games form steam community games: Unless you specify what exactly, nobody can tell. If it's just about stuff for Gmod like TTT or prop hunt, it should be similar as with L4D and Half Life.

Of course all of that are just my assumptions and experiences I had with some of the games and the knowledge I overheared online. So I can't be 100% certain. But most of the issues you might encounter would be accounted by your CPU, a hyperthreaded dualcore is just to weak in some cases.