Yes, HSS will work outdoors with your flashes set up in an E-TTL wireless configuration. However, you'll have two things going against you right off the bat so your working distance is going to be limited to some degree. First of all, under bright sun light, the master will be competing with the sun so its lower powered command flashes may not be as visible to the slaves unless they are close to the master. If the sun is in front of the slave and the sunlight falling on slave's IR sensor, the sun will cause a glare that makes it difficult for the slave to "see" the command flash from the master at longer master to slave distances.
Then there's the fact that, when in HSS mode, the output of the flash is reduced by an amount which depends on the shutter speed used. You'll lose two stops of light as soon as the flash is switched to HSS mode. And then you'll lose an additional stop of light for every stop above the max sync speed you set the shutter speed. For example, if you set the shutter speed to 1/500, you'll lose about 3 stops of light compared to shooting in normal (non-HSS) mode. At 1/1000, you'll lose 4 stops of light.
So just be sure to take these things into account when setting up the flashes outdoors in an E-TTL wireless configuration.