Yes, putting weight over the front wheels into a turn helps a lot. The SI guys most likely drive a lot differently from the R18 crew. Being a low power R18 driver myself I can offer my experience with trying to run hard and fast....
If its an AT you have two things to deal with. The AT itself, which isn't all bad, and the Honda Grade Logic Transmission Controller. Its a great trans for normal driving and its a cruel sadistic bastard if you want to go fast. The car will "neutral out" and completely disengage the transmission if you hit the brakes too hard at speed. It thinks you are panic braking for a crash and need to stop right way. Hence, it disengages the transmission so there is no forward push at all. If you are coming into a corner hot and late brake/stab/stand on the brake pedal you can hopefully catch the transmission before it fully disengages and:
1) You missed it. It fully disengaged. It neutraled out and you scrubbed a ton of speed. Hey you made the corner but now you're going 25 and the trans is stuck in 3rd and it won't drop to 2nd with it floored and its gonnna take you 40 seconds to climb back up to 55mph. Crap. You basically just stalled an AT car. The grade logic controller is examining a bunch of inputs like throttle position, pedal position, the angle of the car, and a whole lot of other factors I don't understand. The car essentially stands still but maintains current speed. I don't understand fully what causes this state but man, its frustrating. You can stop or keep going but it takes a few seconds for the car to "kick back in" and get going again.
Better options:
2) Get off the brakes sooner, cause you braked correctly, and have it start engine braking you with a 5th to 4th (rare) or 5th to 3rd convertor engaged gear drop with hard engine braking. (The RPMs spike temporarily before full neutral release) If you end up mid turn in this state, getting back on the gas quickly generally results in a brief high rpm rev with almost no power. It sucks and you lurch the car hard and it immediately drops to 5th again, duh you revved it hard, and then down to 4th or 3rd or, 2nd if you really boned it, and lost a ton of speed before picking up the power again.
What you want:
3) Be able to get back on the gas and catch a 5th to 3rd drop without losing too many RPMS and the power band on the way out. Limited as it may be if you are able to do this and pull 3k rpms out mid corner you will be ok. You will have full power and be able to easily rev out to 5k before it tries to upshift again. You can absolutely feel this 3rd gear catch if you do it right. Braking properly coming in, which means not full hard brakes, but enough to scrub speed and cause a downshift, that generally drops into 3rd, and turning in semi-early so you can get back on the power mid-turn. Essentially you will catch the trans before full neutral release and be able to hit the gas with 3rd engaged and put down enough power to maintain speed and then accelerate out of the turn.
These cars have no power anyway so don't expect some huge life changing difference if you hit option 1, 2, or 3 on occasion. If you do manage to catch a nice engine braked 3rd gear drop and pull out of a turn and wind out the gear... nice job! Pretty awesome wasn't it? Now if we would all stop being stubborn and buy manuals we could do that all the time. But since we aren't cool like that, we have to suffer most of the time and occasionally have a wicked corner experience and have people say "holy crap man, thats not an SI?"
The third option is the one you want to catch but it doesn't always happen due to the grade logic controller. If the road is flat thats one thing. If its tilted up or down then the car picks a different set of parameters, grade = tilt and logic = computer thinks for you, and the trans responds accordingly for your Grandma's general driving habits. Duh, you granny loves her Civic. Thats why she's bought 4 already and you're only on your first one. Hence, Honda caters to Grans preference, not yours. When you've bought 4 Civics you can call Honda and tell them how you want a more aggy drivetrain in your base model Civic for taking your cat to the vet and going to Target for more Depends. Hell, I bet your Gran would out drive you cause she's got less to lose from crashing and since her sight is fading I bet she comes into corners a bit too hot more often than anyone else.
Other than that if you manage to panic brake the trans into full "neutral out" mode and then get back on the gas hard, most likely you will feel a large jolt from the torque convertor locking up and putting power to the wheels again. Catch it part way and you'll love it. I think you'll probably need a heck of a set of tires to be able to carry this type of speed through a corner but thats my experience trying to wring performance out of an AT R18.
Im sure some smart Honda techs could really tell us whats up and whats going on in the transmission/controller. If I'm wrong then please correct me. I just know what mine seems to do when it gets hot and I'm chasing a pack of Si/WRX/NSX at the Dragon.