The famine was factor in some people’s decision to emigrate but the worst years of the famine were 1847 – 1850, so if they had gone to Scotland before that it may not have been the primary reason. And Belfast wasn’t as badly affected in the famine as other parts of Ireland. People had been pouring out of Ireland all through the 1800s. The famine simply speeded the process up.
The main driver for leaving was to get better paid work. One of Ireland’s problems is a lack of natural resources. There’s no coal, oil, iron ore etc, and so apart from a modest amount of shipbuilding in Belfast and the Belfast linen mills (which mostly only employed women), it did not really get the industrial revolution that benefited England and Scotland where mills, steelworks, ship building, coal mining and all their support industries were major employers creating hundreds of thousands of new jobs. Much better paid than subsistence farming or weaving. Added to that you had the effects of a massive population explosion in Ireland – up from 3 million in 1750 to 8 million in 1841 (no-one is really sure of the reasons why but reduced neo-natal deaths seem to be a factor) and the famine. So some push factors and some pull factors saw huge numbers of people leave Ireland. Something like 2 million people emigrated from Ireland in the 1800s.
If you look at the Scottish censuses for the Glasgow area in the late 1800s, you will see that about every fifth person recorded there was born in Ireland. Scotland was a particularly popular place to go to work because it was easy and very cheap to get to.