can i take the test

You can take the exam, but your issue is that you will not be able to use it.
The problem that you are going to face is with immigration, you will not be able to get a visa to work in the US as an LPN. If you can, it will take you several years, more like five or six. RNs are covered under the NAFTA Treaty and can work with just a TN Visa. You must also have a Visa Screen Certificate and this is not offered for LPNs. The requirement is that you must hold a professional nursing license in your country, the LPN is a technical license in their eyes.

If you are determined to work in the US, you will get things done much quicker with the RN. Almost immediate work visa, as soon as you would pass the NCLEX-RN and have a Visa Screen Certificate in hand.

This has nothing to do whatsoever with Michigan, but US Immigration policies. And you can not work without a visa that will permit you to.

There is no reason to take the LPN licensing exam, it will not help you in any way, you won't be able to use it in the US. Just go straight for the RN program.

Otherwise, you have the right approach.