Answer is yes.
I have seen this question asked and answered before. Typically the answers I see range from very little to none. I had a hard time believing that there was no power to be had, so I did a little test today while I had the TJ on the chassis dyno. I tried to keep it as scientific as possible. I allowed the engine to reach full operating temp before starting and I gave it ample cooldown time in between each pull. I also logged the coolant temp and intake air temp with a scan tool before each run. I did 5 runs with the stock airbox and intake tube, 3 runs with a Edge intake tube and K&N filter, and 1 run with the factory airbox and tube, but with the airbox inlet velocity tube removed. Results.....
Run 1 stock airbox and tube ECT 197 IAT 136 HP 152.3 TQ 193.7
Run 2 stock airbox and tube ECT 199 IAT 141 HP 153.4 TQ 197.3
Run 3 stock airbox and tube ECT 199 IAT 144 HP 153.0 TQ 194.2
Run 4 stock airbox and tube ECT 197 IAT 146 HP 153.1 TQ 194.7
Run 5 stock airbox and tube ECT 197 IAT 139 HP 153.6 TQ 193.1
Run 6 DQ started log late
Run 7 DQ double clicked the start
Run 8 Edge tube and K&N ECT 197 IAT 135 HP 163.1 TQ 201.3
Run 9 Edge tube and K&N ECT 197 IAT 145 HP 163.8 TQ 203.6
Run 10 Edge tube and K&N ECT 199 IAT 152 HP 163.7 TQ 202.1
Run 11 stock airbox velocity inlet removed ECT 195 IAT 143 HP 157.5 TQ 196.9
As you can see the runs are fairly consistent and most are within 1-2HP of each other. Removing the velocity horn from the stock airbox gained around 3-4HP alone. Replacing the stock airbox and tube with the Edge tube and K&N filter was good for a solid 10HP. The gains were most apparent above 4k RPM, but there were small gains below 4k as well. Does a cold air intake add power on a 4.0? Yes, in my testing it was good for around 10HP at the wheels. Is that power worth the money or the possible lack of filtration? I don't know, you be the judge.
I have seen this question asked and answered before. Typically the answers I see range from very little to none. I had a hard time believing that there was no power to be had, so I did a little test today while I had the TJ on the chassis dyno. I tried to keep it as scientific as possible. I allowed the engine to reach full operating temp before starting and I gave it ample cooldown time in between each pull. I also logged the coolant temp and intake air temp with a scan tool before each run. I did 5 runs with the stock airbox and intake tube, 3 runs with a Edge intake tube and K&N filter, and 1 run with the factory airbox and tube, but with the airbox inlet velocity tube removed. Results.....
Run 1 stock airbox and tube ECT 197 IAT 136 HP 152.3 TQ 193.7
Run 2 stock airbox and tube ECT 199 IAT 141 HP 153.4 TQ 197.3
Run 3 stock airbox and tube ECT 199 IAT 144 HP 153.0 TQ 194.2
Run 4 stock airbox and tube ECT 197 IAT 146 HP 153.1 TQ 194.7
Run 5 stock airbox and tube ECT 197 IAT 139 HP 153.6 TQ 193.1
Run 6 DQ started log late
Run 7 DQ double clicked the start
Run 8 Edge tube and K&N ECT 197 IAT 135 HP 163.1 TQ 201.3
Run 9 Edge tube and K&N ECT 197 IAT 145 HP 163.8 TQ 203.6
Run 10 Edge tube and K&N ECT 199 IAT 152 HP 163.7 TQ 202.1
Run 11 stock airbox velocity inlet removed ECT 195 IAT 143 HP 157.5 TQ 196.9
As you can see the runs are fairly consistent and most are within 1-2HP of each other. Removing the velocity horn from the stock airbox gained around 3-4HP alone. Replacing the stock airbox and tube with the Edge tube and K&N filter was good for a solid 10HP. The gains were most apparent above 4k RPM, but there were small gains below 4k as well. Does a cold air intake add power on a 4.0? Yes, in my testing it was good for around 10HP at the wheels. Is that power worth the money or the possible lack of filtration? I don't know, you be the judge.