I think so, at least that was the case with the old models....

Hi MarcelM742,

You can control the signal tones.
Please proceed as follows: MENU → (Camera settings 2) → [Signal tones] → desired setting.
You have 3 options:
On:All:
Sounds or beeps are generated when, for example, the correct focus is achieved by half-pressing the shutter button.
On: Shutter only:
Only the shutter sound is produced.
Off:
No sound is produced.
You can find the operating instructions on our support page.

Sony Europe

Yes, you can.
In the menu "Camera 2" on page 7/7: Set signal tones to "Off".