Unfortunately not. See the last sentence of Wireless Hack.
"If you don’t have the remote hack class feature, you must be adjacent to the computer to attempt your checks."
Certainly implying that you get Wireless Hack's normal range with Remote Hack, otherwise you have to be adjacent.
My table has ruled that it applies. Remote Hack extends the range of computers and engineering checks. Wireless hacking is a computers/engineering check.
Edit because I was wrong, Wireless Hack is at level 5 not 7. I'm a drone mechanic, what can I say?
With that said, Wireless Hack has a range of 20ft, which is accurate at level 5. At level 5, Remote Hack is giving you a wireless range of 20ft. The quote Uchuujin posted clearly links the two abilities, so I think it's accurate to increase the range as you level.
Unfortunately no, the range of Wireless Hack doesn't increase with Remote Hack. At level 15 Wireless Hack's range is increased to 40ft by Multitasking (pg 79). By that point your Remote Hack range is 70ft so the two abilities' ranges aren't the same.
The difference is action economy. Remote Hack lets you try to make checks from a distance. Wireless hack lets your exocortex make checks.
If you are trying to Crack into a computer system and have all the time in the world, wireless hack won't matter. If you have an extreme time crunch, or need to get into a system while combat is going on, the exocortex mechanic can work with their own actions and their cortex to perform a multiple round hack faster, or can set their exocortex to the task of getting into the system while the mechanic keeps fighting off enemies.
Huh, I had apparently glossed over Multitasking every time I checked out the exocortex. Good to know. Wireless Hack has one more use. It allows you to remotely Overload/Override an electronic device in Wireless Hack's range.
I had to to stand next to the murder robot we were fighting to attempt to Overload its biggest weapon while our exocortex mechanic could do it safely across the room. It's a notable buff to Overload and can open up additional uses for it.
Thanks for clearing this up for me everyone!
Happy to help!
Also, I feel it's maybe relevant to reference this thread.
There's been some discussion about how the Wireless Hack ability works with hacking. Seems like there is some consensus that the Wireless Hack ability doesn't quite function as advertised. The crux of the argument is that "hacking" is a full round action, whereas accessing a system is a standard. Since the exocortex gets a standard action, some have interpreted the description to mean that Wireless Hack allows the exocortex to access systems but not to actually hack. This consensus provides that you could commit your move and swift actions to hacking in cooperation with the exocortex's standard and keep your mechanic's standard action. So your mechanic would still have a standard to shoot a gun or swing a sword, but the exocortex couldn't hack independently.
To my mind, this interpretation would make coordinated assault nigh useless for the exocortex variant mechanic. So I think there's a reasonably valid alternate interpretation that this constitutes a "specific rule overrides a general rule" situation, where your exocortex is allowed to hack as a standard. But I haven't gotten much feedback on that notion yet.