IA Version 2.0z does a good job of converting them. I threw all kinds of odd Word tables at it and it converted all, some better than others. For the most part, if your tables have data in each cell, they will convert flawlessly. If, on the other hand, your tables have empty cells and irregular shapes and sizes, look for problems in the conversion. Empty cells particularly cause problems and this is not necessarily IA's fault.
Browsers typically ignore empty cells and create an odd-looking blank space in the table.
If your files have embedded graphics from most any source, IA will spawn a process that converts them to inline GIF files. I found the results to be pretty much as expected, with few surprises. Of course, if your document contains many large graphics, expect some problems in the processing. However, most of my tests passed without a hitch. Basically, if you can import the graphic into a Word file, IA will handle the conversion to GIF and placement in the HTML file.