If you do not pick up the gold, do you lose it?
I tested this myself during a game for weekly quests. It seems the chests will pile up on top of each other as I played 5 rounds without collecting a chest and then ran over it after the 5th round and got 13 gold and a fish bone.
The chests will disappear when you travel to another players board but will be added when you travel back to your own.
I am not sure of the number of chests you can stack and if they start despawning after a certain amount but I can say for certain up to 5 works.