FAR Part 14 makes it clear that bids that do not comply with the IFB are considered nonresponsive. But there are exceptions and clarifications. 

FAR 14.301 (a)  states :"To be considered for award, a bid must comply in all material respects with the invitation for bids. Such compliance enables bidders to stand on an equal footing and maintain the integrity of the sealed bidding system."

Paragraph (c) states:  "Bids should be filled out, executed, and submitted in accordance with the instructions in the invitation".

FAR 14.404-2 indicates:  " (a) Any bid that fails to conform to the essential requirements of the invitation for bids shall be rejected."    If the soliciation called for the bid to be signed, and there was no original signature provided, the bid is nonresponsive and must be rejected. 

However, FAR.14.405 identifies "minor informalities or irregularities" that are merely a matter of form and not of substance".  If these minor informalities are discovered, "the contracting officer either shall give the bidder an opportunity to cure any deficiency resulting from a minor informality or irregularity in a bid or waive the deficiency, whichever is to the advantage of the Government."

Take a  look at FAR 14.405 (c) , when discussing failure of  a bidder to sign a bid. It is a minor irregularity which can be corrected  PROVIDED:

 (1) The unsigned bid is accompanied by other material indicating the bidder’s intention to be bound by the unsigned bid (such as the submission of a bid guarantee or a letter signed by the bidder, with the bid, referring to and clearly identifying the bid itself); or

           (2) The firm submitting a bid has formally adopted or authorized, before the date set for opening of bids, the execution of documents by typewritten, printed, or stamped signature and submits evidence of such authorization and the bid carries such a signature;

  So if the unsigned bid also contains other signed material indicating  the bidders intent to be bound by the bid, or  prior to bid opening, took action and executed dcouments in support of submitting a bid, those actions could be interpreted as wanting to bid and the lack of signature is a immaterial defect. The KO can accept the bid.   But note, the FAR is saying  if the bid isn t signed, there has to be a signature somewhere else.  In the absence of any signed documents to support the bid, it should be rejected.