No, it forms a diphthong with the y -> -wy-, as in wyth (eight). Welsh does not really have silent letters.
Ivona's Gwyneth does not seem to pronounce this one very well, which might not be helping. If you go to www.ivona.com you can type penwythnos into the speech box there and then choose 'Welsh - Geraint' to pronounce the word - it is clearer.
- pen: basic meaning is "head", here means "end". (Also in e.g. pen-blwydd "birthday", which is an "end of a year-of-age".)
- wythnos: week
- wyth: eight
- nos: night
So penwythnos is "week-end", while "week" is literally an "eightnight".