I was wondering if the brightness temperature from band 6 of USGS Landsat 7 Surface Reflectance Tier 1 product in Google Earth Engine Top of Atmosphere Brightness Temperature?
Yes, Band 6 is the top-of-atmosphere brightness temperature.
This can be found from the Earth Engine dataset description page for USGS Landsat 7 Surface Reflectance Tier 1, which links to the data provider's (USGS's) product guide LANDSAT 4-7 SURFACE REFLECTANCE (LEDAPS) PRODUCT GUIDE which defines the product bands. Section 3.5 is relevant:
3.5 Band 6 Top of Atmosphere Brightness Temperature
This option delivers the TOA Brightness Temperature (BT) for thermal Band 6, which is converted to Kelvin.