We can estimate the overhead somewhat by observing that the signatures are going to be maybe 100 bytes roughly, so 2k bytes for all of them. Blocks are currently limited to 64k so this is around 3%. If block size goes up it would be less. (Ignores various details about how transactions and blocks are transmitted around, but close enough for discussion.)
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That was a pretty good estimate, actually. It's done as a regular transaction (eg. has TAPOS data, etc) and it looks like the transaction will vary between 98 and 115 bytes in size (depending on size of account name of the witness).