Apple Watch Series 4 GPS Model

Yes.

https://support.apple.com/en-us/HT204691#watch

This webpage includes instructions for sync'ing your iPhone music to your Apple Watch. It also happens to have information about streaming music as well, which is NOT what you want. Just make sure you read the correct section.

When I first got my GPS only Apple Watch Series 4, I let my iPhone sync as much music as would fit. I had 1,500 songs on my Apple Watch. I have since backed off on that, by telling my iPhone to just sync specific playlists. I have intentionally cut back to 71 songs, and that is mostly so I can demo playing music from my Apple Watch.

I have used 4 different Bluetooth headphones with my Apple Watch. My Airpods, Sony Bluetooth Noise Canceling headphones, 15 year old Insignia Bluetooth headphons, and 15 year old Jabra Bluetooth headphones. Mostly I did this pairing to prove I could do it.

NOTE: to make sure I was playing music from my Apple Watch, I turned Bluetooth off on my iPhone, so there is no way it could talk to any of my headphones.

You might find the following webpage useful

https://support.apple.com/en-us/HT205547

Make sure you read the footnotes

That is correct.

Only if you use bluetooth earphones or speakers.

My pleasure.