Mightytext will only send a text message if my phone's screen is unlocked, so basically it functions as a keyboard for my phone - a keyboard that only works with text messaging, and that you have to keep logging into.
I used this the paid pro version of this app for 2 years... and toward the end I had to login to my phone every time to get the message to send that I had sent on the PC... Made it not worth it in the end... so another issue I was having with it prompted me to go looking for a rival app... and LOW AND BEHOLD... "messages" by google is free and works perfectly with no hiccups!
I find MightyText to be a great Chrome Add-in. It lets me see and reply to Text messages without digging my phone out of my pocket. Also shows in-coming calls and battery level.