They have a CDMA network and LTE so I would assume yes.
You probably won't be able to use telus cdma network because the imei is not in their network. Same reason why the Verizon Note 3 won't work on Sprint.
My understanding is that telus is sunsetting cdma soon anyway.
To answer the op question, since telus has a game network, you should be able to use it. Looks like the Verizon Note 3 supports the same spectrum as Telus on everything but 4GLTE. I believe Telus uses b4,which the Verizon Note 3 supports with the latest update. But I wasn't able to get my note 3 to auto switch between lte and gsm when I used tmobile, though manually switching worked
Telus Note 3 :
4G LTE : 700MHz (Band 17) / 850MHz (Band 5) / 1900MHz (Band 2) / AWS (Band 4) / 2600MHz (Band 7) / 2100MHz (Band 1)
4G (HSPA): 2100MHz (Band I) / 1900MHz (Band II) / 850MHz (Band V)
2.5G (GSM): 850MHz / 900MHz / 1800MHz / 1900MHz
Verizon Samsung Galaxy Note 3
LTE, CDMA/1xEVDO Rev. A (800/1900 MHz)
LTE B13/4 700/1700
Global Network: EDGE/GSM (850/900/1800/1900), HSPA/UMTS(850/900/1900/2100)
dpham00, Android Central Moderator
Sent from my Verizon Samsung Galaxy Note 3 via Tapatalk Pro