If you have enough Catapults (which should be the case after you get Construction), then the Catapult makes a great mainstay unit, and a great 1st attacker regardless of whether you have access to a strategic resource.
The question then becomes, which unit becomes the 2nd attacker? Using the Catapult itself, in comparison to a Swordsman, sacrifices only 1 Strength and +10% city attack, but still allows you to get City Raider. For Aggressive leaders, the Catapult is also 1 promotion behind the Swordsman. The main danger is Horse Archers, which can ruin your Catapults, but you can bring Spearmen to counter this.
The advantage of Catapults over Swordsmen as the 2nd attacker, however, is that you don't need to worry about having too few siege units. Your 1st attacker and 2nd attacker units are the same, and using them as 2nd attacker units (which means that enemy units have already been softened) will allow your Catapults to get more promotions.
However, I rarely find myself in a situation when I have no Ivory, Horses, Iron, or Copper.
I often apply this strategy to the Riflemen age. Often, during the 1st attacker stage, when I use Cannons as sacrificial units, the enemy units are weakened to a point that my Cannons have a good chance of surviving. I have thus reached a "critical mass" of cannons that allow me to defeat the enemy stack without having other types of units.
The same principle can be applied to the medieval age, when you have Catapults instead of Cannons. It's still possible to achieve a critical mass of catapults, but you need more of them since a catapult has a lower strength than a cannon.
The advantage of catapults over cannons, however, is that cannons are easily countered by Cavalry units. On the other hand, catapults do not receive a penalty against Knights, although they do receive one against Horse Archers.