For a normal conditional to work you would have to write it like this:
{if logged_in_member_id == "4333" || logged_in_member_id == "3871"}
However that's not very flexible and isn't going to work with a piped list of IDs. I've written a custom plugin in the past to solve a similar issue. There's a plugin called Pvl Check If on Devot:ee that I think would work in this situation. Your code using the plugin would look something like this:
{exp:pvl_checkif value="{logged_in_member_id}" is_in="{members_field}{id}|{/members_field}" parse="inward"}
<p>Yes Sir!</p>
{else}
<p>No Sir!</p>
{/exp:pvl_checkif}
I'm not sure how the variable pair will go inside the plugin parameter... you may need to play around with it a bit. Perhaps try with hardcoded values first.