Is Bleaching of Teeth Possible if Having Porcelain Veneers?

Initially, the results look very nice, having bleached teeth that get covered with veneers.  But over time, the color will fade, and the dark tooth structure under the veneers will be impossible to change.  It is best to deal with the color restoratively, or only bleach teeth that are not going to be veneered.

In your case, bleaching the adjacent teeth is fine, the bleach won't harm the veneers and might make the adjacent teeth match the veneers.  MIGHT.

Bleaching  teeth that don't have veneer restorations is fine. Just keep in mind that veneered teeth will not change color. Just place the gel in the tray where you natural teeth are, so that you don't waste gel. If you happen to get bleach on your veneered teeth with will not hurt them.  If you are considering replacing your veneers bleach first to your desired "reachable" shade, stop for 10 days to allow color to stabilize then choose shade for your new veneers just keep in mind that you will have to continue to bleach as long as you want your natural teeth to match your veneers.

Whitening (bleaching) products will not affect your porcelain veneer and hence can be used to whiten any adjacent teeth.  But you must realize that no whitening product will ever alter the colour of your porcelain veneers or crowns.  If you have yet to get veneers I would recommend that you whiten the adjacent teeth before the veneers are done so the porcelain colour can match the adjacent bleached teeth. 

Veneers are not affected by bleaching; they will be neither damaged nor whitened.  Only the natural tooth structure itself will be whitened by bleaching.  So keep in mind that after bleaching, your teeth may be whiter than your veneers. But if your veneers are whiter than your own teeth to begin with, then bleaching can work to even out the shades.  Best, Dr. Elizabeth Jahanian

While it's usually recommended to bleach first, to get your natural teeth as light as possible, and THEN match your veneers to that shade, it's perfectly safe for you to bleach after your veneers are placed.  Just know that the color of the veneers will not change with the bleaching process.