That might be one way to do it. Another might be to pursue two bachelor's degrees simultaneously, called a dual major. The key to your situation is that you seek to be accredited in two separate professions: architecture and professional engineering. You will need to meet the educational requirements for each, though there may be overlap.
In the United States the licensing for professions is mainly regulated by each state. The states look to professional organizations to help them set standards and requirements, but ultimately who can be licensed and how is a matter of state law. If you have an idea where you want to live and work you might focus on meeting the specific requirements for that state. Another strategy could be to meet the requirements for those states that have the most stringent standards. This will give you a wide selection states that would be willing to license you.
Here are each states licensing requirements for architects:
And for architectural engineers:
A closing thought qualifying for multiple careers can be very challenging. If it truly matches your desires you may find such a challenge incredibly rewarding. On the other hand if you look very closely at the two fields--perhaps even as you take the college subjects that they have in common--you may discover that you are drawn to one more than the other. If so, consider whether it would be more efficient to focus on that.
I hope you'll discover a satisfying career and that this advice points you to some good things.