The team's three days of running for Pirelli with its 2013 car at Barcelona in May is at the centre of the row that has enveloped Formula 1 since the test came to light over the Monaco weekend.
Mercedes and Pirelli faced the FIA panel in Paris on Thursday, with a verdict due "by Friday" according to Tribunal president Edwin Glasgow QC.
"We are pleased to have had the opportunity to demonstrate that we acted in good faith and made no attempt to gain a sporting advantage," said Brawn.
"We want to thank the Tribunal and its president for a fair hearing and we now await their decision."
Key elements of Mercedes' argument in Paris were that the test was conducted and organised by Pirelli rather than itself, that it gained no beneficial data from the mileage and that as the test rules technically preclude both current cars and those 'substantially conforming' to current rules, Ferrari's recent tyre testing with a 2011 car should also be scrutinised.
The FIA had originally requested evidence from Ferrari as well as Mercedes and Pirelli, before deciding that the Italian team had not breached the regulations.