Cliff - would depend on whether the velocity of the solar system was greater than the escape velocity.
I suppose you could do a rough sum with ve = sqrt(2GM/r)
ok so here is my guesstimate at suns speed around the galactic centre at present
(pi*2*26,000*9.46*10^15)/(225000000*365*24*60*60) - its around 220,000 m/s
2 pi radius of orbit / orbit timeand my guestimate of the escape velocity - it's around 2000 m/s
((2*(6.67*10^-11) * (2*10^30)*(4.1*10^6))/((9.46*10^15)*26000))^.5
sqrt of (2 * Newtons Constant * 4.1 million * one solar mass) / radius of orbitI hereby nominate those for the two silliest sums ever posted. But I make the suns velocity much larger than the escape velocity. that makes sense to me because the supermassive black hole at centre of milky way (in sagitarius) is thought to be pretty small (at 4.1 million solar masses) - so whilst much bigger than anything else - it is drawfed by the addition of all the stars in the galactic centre
And i bet I have made a silly mistake in the maths or the physics or both!!! the sums are clickable to wolfram alpha if you need to correct