Yes, you can. Houghton houses the historical archives of Houghton Mifflin Co., including editorial correspondence, contracts, and 19th- and 20th-century business papers. The archive does not include copies of Houghton Mifflin’s publications.
There are several online finding aids for the cataloged parts of the collection in HOLLIS for Archival Discovery. An easy way to see a list of the major collections is to search for "Houghton Mifflin" and limit to Creator in the 2nd drop-down, below. (Go directly to that search)
Much of the 20th-century part of the archive remains uncataloged, but you are welcome to look at all parts of the collection in the Reading Room.