Hey jimmy,
Any component would consume server's bandwidth and memory on use. I would say it depends on the site traffic. Higher site traffic would definitely drive up the bandwidth, imagine many users sharing files.
Conversekit performs ajax requests at a set interval which can be configured in the plugin settings(
http://take.ms/er3Gg).
The recommended/average value is 4 seconds and a decent server should be able to handle this at least.