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Yes. You can. HOWEVER, you must first fill out FORM1 from the ATF and register your firearm before the building can begin. AND yes, they view the suppressor as a firearm.

Here's the Link to the form to fill out-->http://www.atf.gov/forms/pdfs/f53201.pdf

Now say You didn't like it or it just isn't your cup of tea and wish to recoup the money you invested in it and want to sell it. You must fill out FORM4.

Here's the link to that for future references.-->http://www.atf.treas.gov/forms/pdfs/f53204.pdf

PS-It could help if you print the form out and take it to a local gun shop so they can help you fill out the forms or explain anything.