Is it possible to escape/beat the Yiga clan if they find you in their hideout?

I just did this part the other day, it is possible and there are 3 approaches that I found.

1. Use a really fast one handed weapon. It is possible to stun lock them and kill them before they can whistle and summon reinforcements. It is really hard though, and only managed to do it once. Lightning and Ice help if you have them, but it takes a lot to do the whole hideout this way.
2. You can sneak attack them. I had a couple of Ancient Battle Axe++ in my inventory (60 damage per hit), and if you can get up behind them (Shiekah armor helps for the stealth bonus, or sneaky food/elixers), you'll get a prompt for a sneak strike attack. With a weapon this powerful, you can take them out in a single hit each. Throwing the mighty bananas on the ground to lure them a certain direction (away from the others mainly) does help, although you have to be very careful on the approach. Too much sound or being slightly to the side will cause them to see you when you get close.
3. In the second room only, you can take them all at once. First ascend the ladder and get the pile of mighty bananas on the second floor. Then sneak to the other ladder and climb up to the second floor catwalk, where you can access the pillar in the middle of the room with the chest on it. If you initiate combat from up there, they will teleport up, where you can keep knocking them down to the ground floor. Repeat until they are all dead. This option is REALLY hard and will go through most of your weapons, shield, and probably more stamina than you have (unless you cook lots of stamina food/elixers).

Personally, I found it much easier to just sneak through the whole way, using bananas to lure the guards away from the two doors. Kill the boss in the last room, then you can loot with no resistance on the way back out once the place is abandoned. The drops from the guards are rarely worth the trouble you have to go through.

It is possible, the big guys are powerful but slow, though you need to be very careful since they teleport.

They are slow enough that you can outrun them and defeat the arrow-wielding guys first without too much problem. Then you must be very careful about only challenging them one-on-one and not getting hit.

Ice arrows are indeed a great help. So are show arrow, frostblades and thunderblades.

It is very useful to note that you can murder one of those big guys without him calling for help, if you keep him stunned with ice and thunder, constantly until he's dead. This is fairly easy to accomplish in the first room, but in the second, accomplishing this is probably just as long and tedious as sneaking around using bananas. That's because if anybody else sees you, they will call for help too, even if you're good at keeping the one guy you're attacking stunned consistently.

Once the ennemies are dead the gates open up.

It seems to be hardcoded that regardless of your equipment, buffs, and blessings, any hit from the Yiga Blademasters (the big guys) is a OHKO. If the Yiga spot you, you basically cannot be hit by the big guys at all.

One strategy that's effective but expensive is to use Ice Arrows. This will freeze the Yiga temporarily. Just keep rotating through Blademasters firing Ice Arrows one after the other.