Would the crew have made it back to Earth anyway?

Everything about the Icarus 2 mission was theoretical, this was mentioned several times in the movie:

Searle: Everything about the delivery and effectiveness of that payload is entirely theoretical.

Capa: Between the boosters and the gravity of the sun the velocity of the payload will get so great that space and time will become smeared together and everything will distort. Everything will be unquantifiable.

However, the mission itself is not designed to be a suicide mission. The mission was to fly to the sun; detach and detonate the bomb and return to earth:

Capa: So if you wake up one morning and it's a particularly beautiful day, you'll know we made it. Okay, I'm signing out and I'll see you in a couple years.

Corazon: The O2 productivity is good. In fact, if anything, we're over-producing. It will trail off dramatically when we get nearer. But in truth, we have the reserves to make it there and a quarter-way back.

However because they deviated in the flight mission to redirect to the Icarus 1, unforeseen issues occurred such as the damage to the heat shields, the burning up and destruction of the vegetable/oxygen gardens and pinbacker getting on board Icarus 2.

After this, it turned into a suicide mission with the only goal of reaching the payload point and delivery of the bomb:

Icarus: Capa; warning. You are dying. All crew are dying.

Capa: We know we're dying. Were OK with it, just as long as we have enough oxygen to reach the payload delivery point.

The reason the shield broke up was not from the sun, but from the boosters of the payload. If the mission had gone according to plan, the payload would detach, and then the crew of the Icarus 2 would have 4 minutes to activate their boosters and begin to fly back before the payloads boosters activated. Because nobody was alive on board the Icarus 2, nobody was flying the ship, therefore nobody activated the boosters to begin the return journey. Because of this, the Icarus 2 had not moved, and when the payloads boosters activated after 4 minutes, the Icarus 2 shield was hit with a huge amount of force and heat from the booster, which caused the shield to tear apart and rotate, which exposed the rest of the ship to the sun, resulting in the destruction of the crew module.

It certainly wasn't initially a suicide mission. Several comments made by Capa and Corazon initiate that fact, but in addition, consider the conversation between Trey and Mace;

Trey: "If you rotate that much, we're going to lose Comm towers 3 and 4."

Mace: "Well, it's a good thing we don't need them."

Trace: "We don't need them now; we're going to need them to go home."

At 89% in full sunlight they would not have lost com towers and could have repaired the shield. Even at 95% percent it never came near the repair area, it was just above the repair lights. They could have stopped rotation there, and let Cpt Kenada reach safety. But they may as well have fired the bomb in on remote from 3/4 of the way, seeing as they would have lost everything the moment that bomb shield moved away.