Do I need to cut under door jambs when installing laminate flooring?
You don't have to, but there's not a great alternative to prevent gaps from showing. An "undercut saw" can be rented cheaply at your local tool rental shop. It's basically a circular saw with the table configured for horizontal cuts. Try to run the blade teeth toward the wood to prevent tearout.

You can also use a fine-toothed handsaw with a scrap of your flooring. Lay the flooring on the subfloor and run the saw on top of it, taking care to not let the saw jump and scar the jamb.