No.
No, the iPhone SE doesn’t support 3D Touch.
In some places where 3D Touch would normally be used, you could do a long press instead. For example, you could long press a photo in the Photos app to activate Live Photo mode.
Why doesn’t the iPhone SE have 3D Touch?
By not including the feature, Apple can create a more meaningful divide between their low and high-end phones, they save on material costs, and they can use a simpler design for the iPhone SE.
Designing 3D Touch for a four-inch form factor would require significant engineering time, and for now, Apple don’t think it’s a worthwhile investment.
Can I add 3D Touch to the iPhone SE?
It isn’t possible to add true 3D Touch functionality, as it requires an extra component in the screen assembly.
(If your iPhone SE was jailbroken, you might be able to fake it — but at the time of writing, there is no jailbreak for the iPhone SE. If one becomes available, then you should be able to download the Forcy tweak from the BigBoss repo, allowing a long press to mimic a Force Touch.)
Wrap-up
I hope this answered your question. If it didn’t, please get in touch via the comments below!