Yes, there is a fast-lane for Museumkaart holders at VanGogh Museum.
For the Stedelijk, I walked right inside the lobby and there was an automatic kiosk that I swiped my Museumkaart at and my ticket came out. No lines.
The Rijks was hit or miss and I went multiple times at different times of the day over the course of a few weeks. Early in the day, there was a very long line to just get in the door of the lobby (this was not a ticket line - that was inside the lobby). But with some of the guards, they would let you bypass that line outside completely by just showing the Museumkaart and once inside, I could enter the exhibit space immediately after another guard scanned my Museumkaart. But on other occasions, the guard outside would say everyone had to queue up to get into the lobby.
I purchased my card at a really small museum - just pick one of the lesser known sites that is close to your hotel. For example, none of the historic canal home museums were crowded at all (Van Loon, Willet-Holthuysen), FOAM Photography Museum was also not extremely busy - all are interesting and worth popping in and don't take more than an hour to walk through.