Traditionally yes. I’ve attended many weddings where the groom and the groomsmen wear matching tuxedoes. The only variation that makes the groom stand out is perhaps color of the vest/tie or cummerbund. Sometimes the boutonniere is also a little more elaborate. Groomsmen traditionally should have matching colors to the bridesmaids.
For a cohesive looking bridal party, it’s important to remember that the bride and groom should still somewhat match the colors of the groomsmen and bridesmaids’ attires. (Though in the case of the bride, white matches everything.)
In the end, how much you want the groom’s attire to stand out from the groomsmen really depends on the wedding couple’s preferences. There are plenty of weddings (particularly daytime ones at the beach) where the groom wears a light khaki suit and the groomsmen go without jackets. Despite this, the groom’s party still looks great and "together."