I’ve tested Steam Link connected to a wireless network, using an entry-level Access Point (Ubiquiti UAP-LR – no AC band) – which is better than most home routers – and the results were terrible. Both devices were less than 2 meters away, and still i couldn’t get neither a low latency on inputs nor a stable image quality. The system constantly blurred all the image to compensate the bandwith lack. You must consider that by using a wireless connection, you are exposed to interference caused by other users connected to the network, and also to any other interference on the wireless connection.
Long story short: NO! It won’t – in most cases.
If you are considering acquiring a Steam Link, be aware that a wired connection is mandatory. I’ve setup my Steam Link in a wired connection (1Gbps network), using the best quality, streamed a 1080p game, and the statistics showed that the device were streaming at a 25Mbps rate. So considering the wireless latency, it wouldn’t be possible, even on the best scenario, to have a good fullhd experience.