The short answer is No.

I am sure an actual witness can give a better explanation, but each witness processes "blocks". The top 20 witnesses get most of the blocks, everyone else is vying for a 21st block that they get in some sort of sequence. If a witness misses a block it goes to the next witness. There are ways to track how many missed blocks each witness has if you would like to consider that as you make your witness votes.

There's also the fact that you and I have very little actual voice in who the top witnesses are. Our witness votes weigh based on our SP, just like our upvotes, so the most powerful SP holders ultimately are the ones deciding who the top 20 witnesses are. I'll refer you to a quote from @lukestokes in our @newsteem interview: HERE.

I'd love to tell you differently, but minnow votes, technically, don't matter much when it comes to deciding who gets to be a top witness. As you can see here, the holders of the most Steem Power really get to decide.

Ultimately though, for this issue, the internet speed and reliability of the witnesses does not impact the performance of the main site as far as I am aware. This is also why the blockchain remains intact and accessible by secondary nodes like esteem, busy, and chain, even when the main site is down.