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Is it possible to have a cell on one worksheet that references a cell on
another worksheet to also reflect the FORMAT of the referenced cell? Ie,
if the referenced cell has a red background, the cell referencing it
should also have a red background?
Yes, using conditional formats.
First create format styles with F11, then tell the cell to apply the format appropriate to the value of a referenced cell.

In the example at c2 - n2 are months Jan to Dec, b3 - b12 are 10 salespersons and c3 - n12 are their monthly sales. We want to use colours to quickly see who sold the most and least each month. c15 - n15 show the min sales in each column (and are formatted white on red. This is per style named "Min") c17 - n17 show the max sales in each column (and are formatted white on blue. This is per style named "Max")

In the conditional formatting for each cell c3 - n12,
1. apply style Min if the cell contents = cell in row 15 and
2. apply style Max if the cell = row 17.

What you achieve is 2 cells in each column automatically turning red or blue if they match other cells based on their value, allowing high or low achievers to be immediately recognised.

Hope this helps.

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