The committee was told that while there is a "really strong structure" in place for resettling refugees, there have been cases already where difficulties in securing suitable accommodation has led to them presenting as homeless.
Cosla policy manager Gayle Findlay said the problems with the family visa structure have not necessarily arisen from breakdowns of relationships between family members, but rather from issues such as a lack of space to accommodate them.
Ms Findlay said: "Currently, unfortunately, the only route for those people whose placements break down, or they're unable to stay with their family, is to present as homeless within their local authority area that they may be in."
She said the Homes for Ukraine scheme, operating under a visa-driven system, means people can arrive in Scotland just as the local authority hosting them receives the information required to identify suitable housing - putting pressure on councils.
This was echoed by Hazel Chisholm, housing policy officer for Highland Council, who told the committee her local authority has already identified someone as homeless after their placement broke down.
She said: "We've already had one of our placements fail after just a couple of days, and there's real concern that those guests didn't present in Highland.
"They actually travelled through to, I believe, Renfrewshire and found accommodation with some friends and are going to be travelling to England."
Pat Togher, from the Glasgow City Health and Social Care Partnership, said such a situation is one that has been given "quite considerable thought", but he said it is "unlikely we would be able to mitigate against that in its entirety".
Ms Chisholm suggested the situation is "not in control", with some councils reporting having been contacted by people who are already in Scotland.
She pointed out that with the coronavirus pandemic still ongoing, teams set up to identify available housing have been hit by staff illness, further causing delay to the process.
The impact of staff shortages on timeframes, Ms Chisholm added, is a particular issue in her local authority, which covers a vast area and houses needing to be surveyed are often in very rural locations.
"Sometimes we've been contacted by families who were hosting to say 'my family is already here', and the data will maybe arrive on the same day, so we've people in properties we haven't property checked, and we're not in control of that," she told MSPs.
Neil Gray, the minister with special responsibility for Ukrainian refugees arriving in Scotland, told MSPs on Wednesday that there has been "anecdotal evidence" of people having to return to Ukraine as a result of delays to visa processing.
Ms Findlay said there is "frustration" among people involved in the rehoming process due to confusion over who is operating the Homes for Ukraine system.
She said: "I think there is very little information in general for lots of people because we're working at pace, almost retrofitting systems to a scheme that's already been established."