No. A siege was never going to be tactically viable for Hannibal, no matter what equipment he possessed. Livy even has him say this himself, after Cannae, to his zealous cavalry commander, who wanted to immediately march on the city (Livy 22.51.1-4; cf Polybius 3.86.8). He never had the manpower to fully invest such a large city area: the old Servian Walls were eleven kilometers around, with 15+ gates, and protecting a static defense force of two legions and uncounted thousands of citizens who consistently demonstrated their commitment to seeing the war to a successful conclusion (so coercing a surrender was unlikely). It was impossible to "guard" the city's entire circumference, much less prevent supplies from leaving or entering (so starving the city into submission was out); and it would have been especially difficult for Hannibal to keep the Romans inside-- to muster enough concentrated force at any given gate to prevent a concentrated force to sally forth from within. Romans were prone to constructing a field operations camp (castra), which they could throw together and fortify insanely quickly. In fact, this is what happened the one time Hannibal ventured towards the city in 211: a Roman force came out to meet him and built a castra on his flank. (ancient citation needed) edit: I got distracted and didn't explain about the castra threat. Building a castra in the field outside the gates would pose a sort of mobile "hard point" to a besieging force, a wild card that can't be controlled and can't easily be dislodged. They are a bit like mobile bunkers.

Secondly, "Rome" by the time of the 2nd Punic War was not just the urban center, and Hannibal well knew this. In Livy, he argues that Roman extermination was never his aim anyway (22.58.3). Taking the city and even burning it to the ground would not have erased "Rome" anyway, because there were Romans (and therefore Roman manpower) all over Italy and just as many pro-Roman allies. Actually assaulting the city and winning was resource-intensive and strategically unhelpful as far as bringing the war to a close. Hannibal's strategy of slowly separating Rome from her base of allies was brilliant and was working well for a time. Ironically, the Roman counter-attack on the Carthage urban center, and the Carthaginian anxiety around the possible success of that venture, is what ultimately brought Hannibal back to North Africa.

Most people are familiar with Caesar's famous siege of Alesia during the Gallic Wars. That involved a double-investment: an inward-facing trench which completely surrounded the oppidum, and an outward-facing trench that protected the besiegers from roving enemy forces outside the battle area. Such a scheme could have worked for Hannibal, if he was allowed enough time to get the fortifications in place. He would have needed more supplies than he had--his army was already under threat of starvation even after Cannae; he would have also needed to have time to complete the siege-works without harassment from Roman forces, which seems unlikely. An interesting "what if," though.