Add a background to an Excel sheet (printed)
You mention in the comments that you are open to other solutions outside of Excel.  That being the case, I found Apple Numbers to do well with using a PDF form as a background image.  This requires no outside software to modify the original PDF.
Embedding the PDF
To begin with, select the PDF you wish to use.  If it is a multi-page document, I find it works best to separate the pages by copying them to individual sheets.  (They can still all be printed or exported together as a single document from Numbers.)
This example uses a generic Employment Application.
Create a new Numbers document

Use the default blank template and delete the table if desired.  Later, we will add tables that can offer far more flexibility of position over the PDF than can be done with a conventional spreadsheet table.
Paste your PDF onto the sheet.
Set the size to the Original Size using the button
set the position to 0x and 0y
Lock the image so it does not get moved again inadvertently (It can be unlocked at any time for adjustment, then re-locked)



Change the Print Setup

Enter the Print Setup by selecting File &gt; Print ⌘+P
Set the Page Margins to 0&quot;
Set the Header and Footer to -.5&quot; or -1cm


2021 Note update: Numbers currently does not accept negative values for Header and Footer.




Overlay Tables

Add tables over your fields.  These tables can be independent and inter-connected, meaning that tricks like merging cells is unnecessary.  They can be inter-referenced for calculations just as can be done in Excel.




Formatting Tables
Tables can be formatted to taste.

Remove borders
Change font colors
Use formulas

With a little creativity, I think you would be easily able to use Numbers to create your documents.  I would recommend the creation of a template for future use if you need the same document over and over again.
Tip: Saving the finished document as a PDF. Use the Print Dialog to export as a PDF rather than the PDF export feature in Numbers.


Resulting PDF