Would a Smart TV with wireless connectivity and an ARC HDMI output be about the same as an AVR with the same capabilities?
Wireless connectivity is exclusively a network item. It is a way to connect Internet enabled devices, such as a smart TV, or your Blu-ray Disc player, or a laptop to the Internet and your home network without wires. It should not be confused with a video connection such as HDMI. You can't get full Blu-ray quality video from a wireless TV connection.
Audio return channel (ARC) is something completely different and is designed to allow you to feed a ARC enabled A/V receiver surround sound from an ARC enabled television. It does not support HD audio from what I have read, but does support other surround sound formats. At this point, it appears that ARC requires that HDMI-CEC be turned on. (stupid requirement)
If your goal is to have a surround sound setup in your home, then you need an A/V receiver. A TV is designed to power the speakers inside the TV exclusively. It doesn't run external speakers or a subwoofer. It doesn't have the connectivity for that. So, if you want surround sound of some sort, then you will still be required to have an external A/V receiver.
If you are in the middle of construction right now, and your A/V receiver won't be near your TV so you can run wires easily later, then you should install 2 HDMI cables and 3 cat-6 cables between the A/V receiver and the TV, and you should run networking to both locations from your network router location or a central network switch location.
...OR....
Run 1.25" or large conduit between the TV and the A/V receiver location so you can put in cables later.
You still will want a hard wired Internet connection in place no matter what.
Wireless, on A/V devices, generally sucks. You want to use the hard wired connection.
Keep in mind that wireless pretty much is just for certain specific features which vary from device to device and from TV to TV. Some TVs can connect to some Internet enabled applications (Netflix) while others can stream photos from your home network. Still others can download all sorts of applications for Internet usage, and play back photos, music, and videos from your home network.
The quality of these players and the functionality offered from TVs, A/V receivers, etc. varies significantly from product to product to product. Many people find that building a dedicated home theater computer (HTPC) is a great way to do things. Others buy dedicated media players such as Dune or Popcorn Hour. Some people prefer dedicated Internet streaming devices such as Roku. While others may prefer the iTunes-centric AppleTV with AirPlay.
The only thing I can say is that during construction, get your wires in place where you want/need them. Putting in a few extra wires now, that never get used is a lot better than wishing you had run one or two extra wires that were never run. It can cost thousands of dollars to get new wires in place in the future and just hundreds to put them in now.
What your specific goal is will determine how everything should be setup.