If there is a pullup then your pulldown will have to be several times stronger 
to make sure that the floating value becomes a logic low. You now have an 
effective voltage divider with a pullup / pulldown configuration.   Fighting 
against the configured on-chip pullup is going to mean that to output a high 
you're going to need many times the drive current you would normally need as 
you sink current into that low-value pulldown resistor.    

Not sure what your threshold on the buzzer is but if the pullup is say 30 to 
50K then to get a solid 10% default low on the pin you'd need a 3 to 5K 
resistor on the pulldown.   That would be a 1.1 to 0.6mA load on the pin when 
it swings high.  You're also burning 0.1mA when the pin floats since the 
voltage divider will always be present.   That may or may not impact your 
design.

Assuming I'm thinking of this correctly.  

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