Right way to convert 120VAC to 5V?
I highly recommend reading the datasheets for any electronics because they have an incredible amount of information.

Short Answer, No

If you read the datasheet for the Particle Photon, it recommends no less than a 1A power supply. Unfortunately, the datasheet for the AC/DC Converter you found shows it has a maximum output current of 30mA, which is nearly 30x smaller than you would want for the Photon.

How to Make This Work

Because you're trying to get ~1A @ 5V and you're working with 120VAC, you don't have to reinvent the wheel--or in this case, the USB Charger Brick!

Literally any off-the-shelf USB charging brick for a phone or tablet will work. I can't think of any that are less than 1A-rated anymore, but if you want a hobbyist-level supply, something like this one may be right for you (not to plug for Adafruit, though they are a great learning resource).

Basically, you'll have a box that houses the Photon and the relay. You simply put this in the box with it, and voila! you have 5V power for the Photon.

Bonus Points

You can even go nuts and remove the device from its housing (DISCLAIMER: This may void the UL listing and any warranty) and just grab the innards to package neatly in a nice enclosure.

EDIT: 

Easiest Solution
Just install one of these at the receptacle you intend to use.