Sure. Create a light entity and use different display pages for the on and off state. It’s even possible to change contrast (which has more or less the same effect of brightness in a ssd1306)…
light:
- platform: monochromatic
name: "OLED "
output: oled_bc
id: oled
on_turn_on:
then:
- display.page.show: page1
- component.update: ssd1306 #the component id which need to be updated
on_turn_off:
then:
- display.page.show: page2 # a empty page....
- component.update: ssd1306
output:
- platform: template
id: oled_bc
type: float
write_action:
then:
- lambda: id(ssd1306).set_contrast(state);