Android
Yes. In addition to supporting end-to-end encrypted messages and calls with other Signal users, Signal Android can be configured as your default SMS/MMS app.
How do I manage Signal as my default SMS/MMS app?
In Signal, tap your profile 
> SMS and MMS.
- To make Signal the default, tap SMS Disabled.
- To remove Signal as the default and to switch to another SMS/MMS app, tap SMS Enabled to select another app.
When Signal is your unified messenger:
- In your contact list, both Signal contacts and non-Signal contacts will be displayed. A blue letter in the outside column will indicate it is a Signal contact.
- Learn how to distinguish when communication is private (Signal message) or insecure (SMS/MMS).
When Signal is not your default SMS/MMS app:
- Your Signal contact list will only list other Signal users.
- Only private messages will be sent or received in Signal.
My Signal contact is offline, how do I send insecure SMS/MMS?
You can tap and hold or long-press the send button on Android to switch to an insecure SMS which will have a grey send button 
.
My SMS/MMS is not sent, what do I do?
Text messages sent through your mobile SMS/MMS plan are insecure and need your phone to be connected to your mobile network. Follow steps to troubleshoot sending messages.
iOS
No. You can not send or receive insecure SMS/MMS with Signal on your iPhone, iPod Touch, or iPad. All communication through Signal iOS is private. Apple does not allow other apps to replace the default SMS/messaging app.
Desktop
No. Signal Desktop does not send or receive insecure SMS/MMS messages. Only Signal messages will be sent or received. We want to encourage users to move away from insecure legacy protocols.
The desktop app is an independent client that works whether or not your mobile device is present or online. You will still need Signal installed on your phone for full functionality like managing groups, read receipts, linked devices, etc.