It is always better to get protection on your gadgets that way their fixing or replacement is prompt.
They do fix them but might want to consider getting their service plan before doing so. It will save you some money in the long run. Monitors also might take them a few weeks to fix (send out, etc). If you need a quick turnaround, they might not be the best place for it.
Most of geek squad won't be able to fix monitors unless you bought it through best buy and got the warranty on it. It also depends on the issue.
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