No. Since when you create photo albums by using photos from PhotoStream the album only is a pointer to the photo ub PhotoStream
You can delete photos from your photo stream the same way you delete other photos from your iOS device or Mac. Just select the photos you want to remove, then tap the trash icon or click Delete. On your PC, select the photos you want to remove from your photo stream, right-click, then select delete. When you delete a photo from My Photo Stream on one device, it will be removed from the Photos tab and your albums and iCloud. Photos imported from My Photo Stream to other devices won’t be deleted. Learn more about deleting photos.
If you sign out of iCloud or turn off My Photo Stream on an iOS device, all the photos in the My Photo Stream album are removed from that device. Any photos from My Photo Stream that were imported to the Recently Added album and the Photos tab will also be removed. The photos from My Photo Stream on your other devices aren't affected. Photos from My Photo Stream are saved on the iCloud server for 30 days from the date you uploaded them to My Photo Stream. If you sign in to iCloud with the same Apple ID and turn on My Photo Stream on another device, those photos will automatically download to this device.
My Photo Stream FAQ - Apple Support