If it did not burst from the internal pressure of the helium gas it would accelerate at a rate proportional to the gravitational acceleration of the gravitational field in which it is present in the absence of other forces.
But....if a helium ballon was taken into space and let go, and if it doesnt float in a vaccum does that mean it will sink? if it will, surely it will find the end of space, is it truly infinite?
Man this is like working out events from Back to the Future.
any balloon taken outside (for example) the space shuttle would vanish instantly as the internal pressure would cause it to expand so quickly that the external pressure (vacuum (ish)) would not be able to hold it together - IT WOULD EXPLODE
if you created a vaccum on earth then no, the ballon would fall to the ground. The reason it floats in air is that helium is lighter than air. same reason why plastic sinks in air, it is heavier.