Not a lawyer, but somebody who went through the greencard process.
The answer is yes. Same for E3 (for Australian).
The risk is once your company files I-140 petition (petition for immigrant workers), you might be denied entry if you leave the US. It's hard to prove your non-immigrant intent... So if you have less than a year on your i-94 it's risky (i-140 takes a while these days to process - mine took 1 year). It would take a few more months to get the EAD and advance parole document before you can travel internationally. So consider these factors as you will have to miss visiting Canada in the meantime.
My friend who was on E3 went through this and his i-94 was running out so he was told he might not be able to work while the application is still pending (the company did offer to continue paying him though, which was nice).
H1B lottery is safer, but the chances are low. If you have a committed employer + stable job then I'd go with the adjustment of status route.
> friend managed to stay in the country despite his i-94 running out.
His adjustment of status was pending so there's a grace period (check with your lawyer). He was basically waiting for his EAD/Advance Parole card at that point!
(IANAL) Once your I-485 is pending you can remain in the US for as long as it remains pending, on that basis. [1]
Most people also file an I-765 and I-131 alongside the I-140, I-485 and I-693 forms, and once approved, you'll be issued an EAD/AP combo card which entitles you to work in the US and return to the US on the basis of the pending I-485. This travel and employment eligibility is separate from any previous E-3 or TN status.
Once you file, you no longer have to maintain your previous nonimmigrant visa status, but if you don't, a rejected I-485 would subject you to immediate removal. If you do, you can return to your old status.
The answer is yes. Same for E3 (for Australian).
The risk is once your company files I-140 petition (petition for immigrant workers), you might be denied entry if you leave the US. It's hard to prove your non-immigrant intent... So if you have less than a year on your i-94 it's risky (i-140 takes a while these days to process - mine took 1 year). It would take a few more months to get the EAD and advance parole document before you can travel internationally. So consider these factors as you will have to miss visiting Canada in the meantime.
My friend who was on E3 went through this and his i-94 was running out so he was told he might not be able to work while the application is still pending (the company did offer to continue paying him though, which was nice).
H1B lottery is safer, but the chances are low. If you have a committed employer + stable job then I'd go with the adjustment of status route.