Can wordpress post and sidebar remain visible after scroll?

Sounds like a fixed position and 100% height are what you’re after:

position: fixed;
height: 100%;

The TwentyFifteen theme uses the following code in style.css:

@media screen and (min-width: 59.6875em) {
    body:before {
        display: block;
        height: 100%;
        min-height: 100%;
        position: fixed;
        top: 0;
        left: 0;
        width: 29.4118%;
    }

    .sidebar {
        float: left;
        margin-right: -100%;
        max-width: 413px;
        position: relative;
        width: 29.4118%;
    }

    .site-content {
        display: block;
        float: left;
        margin-left: 29.4118%;
        width: 70.5882%;
    }

Alternative: I’ve been using the 2015 theme and trying to get the left, persistent navigation sidebar to scroll independently of the content, instead of the default behavior.

From a user experience perspective, the user is scrolling the content, not the menu. When both sections scroll simultaneously, the user is encountering a lot more information, when they probably just want to see more of the main body.

If you interested in this alternative, see this SE thread.