Yes, you should be able to download and copy Excel spreadsheets from the web to Numbers on the iPad; with a reasonable level of compatibly.
When you tap on the link in Safari the file will be downloaded and displayed in a QuickLook tab, still in Safari. At this point, the file is not saved. You should see some Open In options at the top right of the webpage. If not tap in the center of the screen to call up the options.
If Numbers is installed it will usually be one of the two options. For other apps choose the generic Open In button, and it will list those that are compatible.
I went to the office.microsoft.com site and chose an Excel template for my test.
I was able to download and open a template in Numbers. It warned me that there had been some font changes, and that the appearance my have changed. This is pretty typical for importing any Excel spreadsheet to Numbers. You can only try and see what happens. In most cases, as long as the spreadsheet does not use advanced features, the import will be usable.
It is possible o copy the file to Google Drive using the Open In option. However Google Drive (Google Docs) does not edit Excel spreadsheets, or maybe it's just the templates. At any rate I was not able to open the file on the iPad either in Google Drive nor via the site in Safari. Not even on the Mac. I even tried Chrome on the Mac. If there is a way to convert the template to Google's format from the site, it's too well hidden for me to find; at least in the few minutes I spent exploring the forum.
There is probably some way to convert the document; another app, Google site, whatever. But I don't have any real suggestions on where to look; other than to Google it.
It is possible to use the Open In feature in Google Drive to copy the file to yet another app. So if you were wanting to use Google Drive to save and share the document, that's still an option. You just can't edit there.
There are other Office compatible apps for the iPad. Those should work just like I described Numbers working, if you should decide on one of them instead.
Good luck.