Alonso was fortunate to escape serious injury in Melbourne after colliding with the Haas of Mexican Esteban Gutierrez in an accident that halted the race.
A three times winner in Bahrain, but unlikely to be chasing much more than a top 10 finish this time as McLaren battle back from a dismal 2015 season, the Spanish driver said the team and Honda had made a "massive effort" after the crash.
"We're still pushing to bring upgrades to each race, so providing we can get everything to the car in time we'll be aiming to get as much track time as possible with the new chassis from the start of free practice," he said on Tuesday.
Honda's F1 head Yusuke Hasegawa said the power unit had been recovered but initial investigations showed the engine and surrounding parts were too badly damaged to be salvaged.
"We will be replacing the complete power unit in Bahrain," he said.
Drivers are allowed five power units to last the complete 21 race season, with penalties if they exceed the allocation.