Yes, you can download to your Android Tablet and have them available offline.
Safest would be
1) Get Nook for Android App and download there.
2) Download Nook for PC and download books there. Move those books over to your Android tablet.
Then you have two sets fo downloaded books
A) Those downloaded in Nook for Android.
B) Those moved over from PC.
The first should work. Nook for Android books do get downloaded to the tablet. But in case something goes wrong you can use the second set.
You may occasionally find a book that won't work with the Nook App. To be sure, when on the books page click on the question mark by "Available on Nook devices and apps" and it will tell you what it will work on.
Having multiple backup copies of your eBooks is always advisable. A) the 'cloud' may not always be available. B) the vendor you purchased the eBook from may not always have the rights to sell eBook. If they lose the rights to sell it, you may not be able to redownload it even though you previously purchased a license to use it.