If Mundy didn't tell Sirius about the guard duty Sirius would have been so angry that....don't want to imagine! But I doubt he would ever welcome Mundy again in his house (that would be the first time he agrees with Mrs Weasley ;-) No, I don't think so! After the dementor thing Sirius would have hated Mundungus if he didn't tell him, and if he told him he wouldn't have skipped his duty!
But good point, though...Mundungus skipping his duty could be important! It seems to be one of the sweet little details everyone overreads before it turns out to be the solution!