Just for clarity of the conversation, Art. 1, Sec.9 - the so-called, "Emolument Clause" - prohibits, primarily, the accepting of titles, emoluments, and "gifts" from any "king, prince, or foreign state". Or, more broadly, foreign entities which may be regarded as states and/or state apparatuses. As well, § 7342 (the FDGA) prohibits the tendering of "gifts" and/or "decorations" from the following sources:
As such, it is a difficult argument to characterize the Nobel Prize Committee by this particular rubric. However, in the case one makes that argument, the definitions set out in (c)(1)(A)(B) render it possible to accept the Nobel Prize:
Now, without superfluously defining what "gift" and "minimum value" denote in the FDGA, I feel confident in saying that the acceptance of the Nobel Prize does not fall beyond the parameters of either Article 9, or the FDGA.
The issue of whether or not Obama is meritorious in this instance notwithstanding, it would certainly be legal to accept the award; and, as far as I know, the amendments to the FDGA in 1977, 1978, 1986, 2002, 2004 and 2006 do not alter the legality of his (potential) acceptance.
Personally, and making my decision based upon even modern renditions of the Prize Committee's criterion, I do not think he deserves this award per se; however, speaking strictly from the standpoint of culpability, he is doing nothing "illegal" by accepting the gift.