The Army Corp of Engineers will still have to get all the environmental impact statements. President Trump cannot override legislation. This has to go through a legislative process.
EPA plays a unique role in the National Environmental Policy Act (NEPA) process. (click here)
The EPA oversees the policy. It is law. The EPA enforces the law. The enforcement is not an option, that is called corruption. The reason approval may have a lengthy timeline is because the company/person(s) seeking to build is in violation of the law. The law is there to protect everyone, including those in violation of the law.
I have no doubt there will be plenty of lawsuits. There is usually a lawsuit involved with these projects anyway.
There are still state and local regs to follow as well. I am sure President Trump already is receiving expedited projects since the signature.