Yes, this is possible.
Pulse SMS centralizes around the idea of one "primary device" for your account that all SMS/MMS communication has to go through. This device is your connection to your carrier and the phone number associated with your account. Messages from other devices are just forwarded to this phone to make the carrier connection and send your message.
Whenever you log in with a device that has a phone number, Pulse SMS asks you if you want to set the new phone as the "primary device."
To set up your work phone to be able to text through your personal phone number, we recommend the following. This assumes you want to text through the personal phone's number from your work phone. You can change the devices to whatever you want, of course. This is just a generic procedure, using work and personal phone as an example:
On the personal phone, create the Pulse SMS account. (If you have already set up an account, we recommend just deleting it and starting from scratch with these steps. Google will restore your purchase.)
After creating an account, you will be notified that it is uploading your messages. Wait for this upload to be complete.
Install Pulse SMS on the work phone and open it up. You will need to set Pulse SMS as the default messaging app on the phone as it goes through the initial import.
On the work phone, go to the top link in the navigation drawer, Text from any device, and log in to the account you created on the personal phone.
After you log in, it will ask if you want to set this phone as the Primary Device. Say "No" to this prompt.
Pulse SMS will download your messages to the work phone.
On the work phone, you should then set the stock messaging app as the default messaging app. If you do not, you will not receive messages to the work phone number.
You have now set up two phone devices on one account. You can use Pulse SMS on the work phone to send messages through your personal phone and view the messages from your personal phone. If you want to send and receive messages from the work phone's number, you will need to use the SMS app that came with your phone. The Pulse app on your work phone will not handle both numbers simultaneously.
NOTE: If your two phones are the same make/model, you will need to install this version of the app on the second phone (non-primary). Otherwise, it will never prompt you to set the phone as the primary device. With the Play Store app version, Pulse SMS will automatically set the new device as primary if it is the same make/model as the old one.
Pulse SMS - I have two (or more) phones. Can I use this app on my work phone to text from my personal phone number?
Yes, this is possible.