Nope.

As a general rule with steam packs, unless it specifically says you'll get spare copies you won't.

I added it to my cart, and on the Review + Purchase page it states:

You already own the following items in "Serious Sam Complete Pack". You will not receive extra copies of these items when you complete this purchase:

◾Serious Sam 3: Jewel of the Nile

◾Serious Sam 3: BFE Bonus Pack

Does this mean I will receive extra copies of all the other games?

To all those people above: You will get the extra games from this pack. Steam says you won't but I can confirm that you do.

See here, here, here for other people confirming.

This is one of the rare exceptions, Serious Sam Complete Pack does provide extra copies for existing games. Steam doesn't tell you so.

wouldnt buying it as a gift just give you everything?

Look at the steamDB.info.
You will get extra copies for the base games, not for the DLCs.