AV3.2 runs in WINE 1.0.1: http://appdb.winehq.org/objectManager.php?sClass=version&iId=22816 -- I can't verify this.
AV3.1 seems to run in WINE 1.2.2, Ubuntu 10.4. On my system there seems to be a problem with character I/O and fonts - many text fields are garbled. But otherwise generally seems to work.
You might also consider ArcExplorer Java Edition for Education (AEJEE, pronounced "edgy"): http://edcommunity.esri.com/software/aejee. This is a Java bundle which runs on Mac as well as Windows; and I did get it to work on a Linux system once. AEJEE supports network mapservers (ESRI ArcIMS only unfortunately) and has a "Catalog" function which makes it somewhat more like ArcGIS with training wheels -- but if you're really interested in ArcView on Linux you should probably try WINE again.