The best resource for this sort of question is the Software Advisor:
http://tools.cisco.com/Support/Fusion/FusionHome.do
Starting from "Find software compatible with my hardware", I tried to build a 1720, and to put a 4ESW in WIC slot 0. But I did not find the 4ESW in the dropdown list. When I did the same with a 1721, the 4ESW was in the dropdown list.
So the conclusion is that you are right: the 4ESW will go in the 1721 but not the 1720, and there is no software version that will make it do so.
The 1700 series design tool does not even list the 1720 any more:
http://www.ciscowebtools.com/1700sdt/child/1.0/index.asp
According to the 1720/1721 data sheet, only the 1721 supports 802.1Q VLANs, and that may be the reason:
http://www.cisco.com/en/US/products/hw/routers/ps221/products_data_sheet09186a00800920ec.html
Hope this helps
Kevin Dorrell
Luxembourg