Posted from Voyager on Android.
Failed to load media :,(
Yes, it works just like any other image.

Some instances might not support uploading them. In that case you would have to host them somewhere else.
Edit: It also works with mp4 and webp.
Edit 2: Here, try it with this one:
https://swg-empire.de/pictrs/image/0d968fba-f087-46e7-9043-16d5bd178dc1.gif
https://catbox.moe/ is great for gif hosting.

gives you:
Oh I get it now, you have to have the gif locally stored on your phone to upload it as an image with the image function.
If you want to embed a gif hosted by giphy its not as pretty.
If you have the direct gif url it should work fine.
Giphy works. You just gotta do it exactly like: 
On Voyager, I type the gif comment then tap the ••• button, “preview” to make sure it looks good before posting.
Giphy works. You just gotta do it exactly like:
Escape characters (\) are handy 
You forgot the exclamation mark.
Is there a native button you’re selecting from within the app? When I click the image button on Voyager it looks like a normal upload file type function.
Press reply, select the first icon on the toolbar, browse to the picture and attach it.
What are you having trouble with?