That board is not good enough.
MCP1703 linear IC regulator 3.3V output's max output current is 250 mA.
Yes, I see now that the MCP1703 is rated to only 250mA. The maker claims his UART supplies up to 400mA at 3.3V. Have one here, I'll run Mark B's wifi load test and get back to you. Might be that this unit is ok for an Omega set-up, but not best for an installation.
@MultiDJRoni While the display you reference (http://ebay.eu/2brESNp or http://ebay.eu/2bYf3pA) communicates via I2C and is potentially controllable from the Omega, I don't know whether or not the chip/display it uses is the same as or compatible with that used in the OLED expansion. If it is not, you may be up for additional coding work to control it from the Omega (not a totally trivial task).
I still think you would be better of using a Prototype Expansion (http://www.robotshop.com/en/proto-expansion-for-onion-omega.html) between your Expansion Dock and OLED Expansion and wiring the Prototype Expansion to provide access to the I2C lines (GPIO 20, GPIO 21, 5v, Gnd) and other pins you need for access to your other devices.
That is a great example to work from. Thank you.
Only problem I have now is trying to convert the temp into F.
I have tried adding the calculations in everywhere I can think of and I just get errors.
Any help would be great. I am real new to python programing.