The short answer:
No, you probably need your phone on to send messages to those particular friends.
Longer answer, incase you want to know why:
It's all about the green bubbles and the blue bubbles.
There are two kinds of messaging; SMS and internet. (There may be more, but not for the purposes of this issue).
SMS is old. It's part of the cellular phone network and works with pretty every phone since the late 1990's. It only works with a phone.
Internet messaging is broken up into different services; What's App, Facebook Messengar, Google Hangouts, Skype, and dozens of others; including Apple's iMessage service. These services only work with themselves. You have to have the same app installed on every device you use. And they only work if you have internet service.
Apple's Messages app does a bit of both. By preference it uses the iMessage (internet) service; but this only works with other people who are also using an Apple device (iPhone, iPad, Mac). When it can't use iMessages it falls back on SMS, when it can. For the most part that means when you are using your iPhone.
Until a couple of years ago, you couldn't use Messages from an iPad with non-Apple devices; because it's not a phone, and it does not have a valid you-can-call-it phone number. Then Apple got clever. They decided that if you have an iPhone, you should be able to use the iPhones SMS capability on your iPad too, so they linked your iPhone to your iPad in Messages (through Apple's servers).
But. . . since the SMS messages still go thorugh your iPhone, it still has to be on. (And using the same iCloud ID as the iPad).
Back to the green and blue bubbles.
When you send something to a friend and you see a blue bubble, that means your friend has an iOS device and you are communicating with them through Apple's iMessage service. When the bubble is green Apple can't find your friend's number in their iMessage service, so they send an SMS message through the cellular phone service, and it's got to use your iPhone to do that; because SMS only works on phones.