Is this a right turn lane or a center turn lane? It makes a huge difference.
Maybe for a right turn lane.
NO for a center turn lane (unless turning nearby).
We have a bike path in Springfield that transitions from bike path to turn lane and back to bike path (with minimal markings).
https://www.google.com/maps/@44.0817...7i16384!8i8192
Scroll forward.
It isn't too bad. I usually ride just left of center in the turn lane to indicate that l am going straight.
If you do choose to ride in a turn lane, ride to the left side of the turn lane when approaching intersections, and use hand signals to indicate turns.
Watch the traffic and be careful at intersections to make sure a car doesn't assume you are turning and pull across your path.
As far as narrow 3-lane roads with a center turn lane, those actually aren't bad. Just ride to the right, and cars can pull into the center turn lane to pass with minimal difficulty if the lane is clear.
We also have some bus lane/turn lanes. I've ridden in them, but only for short distances. Keep a lookout. A bus technically would have the right of way over a bicycle that is poking along.