Celeron 887: Will this CPU play 1080p videos easily?

Celeron cpu`s are not the best type of cpu for decoding 1080p video, the other factor to playing HD 1080p videos has to do with the type of graphics card you have. Try to avoid using any on board graphics solution as most have trouble playing HD if the motherboard is quiet old.
 
Assuming the video end is up to snuff, which being as I saw Intel HD graphics is may not, then you should be able to play on that.

I remember with a proper graphics card a 3GHz P4 was what most players used to require to do 1080P. I would think a 1.5GHz Sandy Bridge cpu with 2mb of l3 should be about that.