Yes, but you'd have to first assign a named range.
For example, you can't use ='Other Sheet'!A1>5 as a criterion for your conditional format, but you could set (via insert --> name --> define) the named range my_cell to refer to ='Other Sheet'!A1 and use =my_cell > 5 as your criterion.
What I am trying to do is turn the background color of a cell one color or another based on if a text string is in a column of data in another spreadsheet in the same workbook.
You showed me how to Define a cell and use that one cell as criteria in my conditional formatting. What about trying to Define a group of cells and including that Definition into a more complicated formula than a simple logic one? Is that possible in Conditional Formatting?
MATCH(A1,my_range,0) will either return a number (the position of the match) or an #N/A error (if no match is found). So, ISNUMBER appropriately maps those possibilities to TRUE/FALSE values for use as the basis for the conditional formatting criterion.