Yes. The Microsoft Publisher 2010 will be compatible with Windows 8 (32 bit and 64 bit). You will be able to open files that were created using MS Publisher 2007 in the 2010 version but it is possible that they cannot be viewed correctly. If this happens there are some things that you need to do. Open the file in Publisher 2010, place the cursor in the text box from page 1 of the document and press Ctrl + A to select all the text. With the text selected, go to Home -> Paragraph -> Tabs and click Clear All. Click OK and save the file under the different name (to keep your old file as a backup).
