In Sicily, you had this reluctance but aslo the fact it was far from Rome, and the roman senators and land-owners didn't cared that much. I'm pretty sure that fugitive slaves outside Roman "Empire" would be even less cared about, or maybe with a "Good riddance" reaction.
I really don't see that a slavery-heavy setup like Rome could afford to let slaves get away with a revolt. Its the top one thing you'd want to discourage in a slave-using nation. The slaves have too little to lose and too much to gain.
But what about a whole fleet didn't noticing the coast?
I don't put your experience in doubt, but the Hercule's Pillar are a tiny, tiny straight. You can't just miss the coasts as they're just before you.
It is possible, although not easy. When you normally sail for pleasure it is easy to forget how many sorts of unpleasant weather you may have to sail in when you do it for a living. A heavy rain can cut visibility to a couple of meters. As can fog. (And a proper snowfall can do worse, although that shouldn't be an issue here). A moonless night can be pitch-black, you'd be entirely dependent on there being settlements with lights on the shore. And even a moderate rain could obscure them.
In daytime you can get an overcast so thick, you cannot see
where in the sky the sun is.
However, I am not advocating that the fleet get lost in the straits of Gibraltar

That is a bit like getting lost on the stairs in a two-floor building. Leaving the straits of Gibraltar, sailing along the coast and then losing it due to poor visibility, poor navigation or poor weather is more reasonable.
Now, I must quite agree that on the face of it, sailing up the coast of Spain to Gaul seems a far more sensible strategy. So we need a reason or a butterfly for that. Perhaps if Spartacus obtains his ships, Pompey is never asked to return from Spain to support Crassus?
Or Spartacus tries to throw Rome of the scent by sailing through the pillars in broad daylight, and turns south for the cities of north Africa. But then turns west as soon as he is out of sight, intending to double back and sail north below the horizon, returning to the coast once he is north of Gibraltar again? It is a Spartacus sort of move, except he'd be overestimating the ability of his navigators...
A landing in West Indies would imply people to land. Without enough food, enough water and enough motivation ("hey, what about being in the total blue ocean for 3 months without the slightest clue about where we go"), maybe the ship could reach some island, but most probably no people aboard.
You are overestimating the time it'd take for a crossing. Of course, any fleet of Spartacus is going to be a pretty ragtag collection of ships, most of which we do not know the speed or abilities of.
We do know, however that the winter speed of the Canary current mean that the time to drift from the Canaries to the West Indies is about 78 days. That is no sails, no rowers, just drifting, so it'll be the absolute maximum.
You average war galley can do a fairly sustained speed over time of 4 knots on rowers alone. That'd mean 26 days to cross. The Trade Winds winds here go exactly the same direction as the current and are strong and sustained. Most of the ancient writers indicate an average speed of 4-5 knots under favorable winds (Transactions of the American Philological Association Vol. 82 (1951), pp136‑148).
So an undamaged ship could cross in 3-4 weeks. The distance would be about 2,5 times as long as the longest Mediterranean trip directly referenced historically.
This is not ASB. We may have left the placid sea of the Highly Probable here, but we're not quite into the choppy waters of the Highly Implausible. Going back, though....thats a different kettle of fish.
Of course, the above assumes that the ships will continue to follow the winds and current once lost. Ships that try to return, or otherwise go off in a different direction are in even worse trouble. Now if the ships are lost, following the prevailing winds makes sense. Its how you cover the greatest distance, and hence maximizes your chance to find land. I don't see anyone trying to fight wind
and current, but I could see ships being lost trying to go south or north.