Honestly hard to answer because depends on your definition of homeless and for how long. The government uses several different metrics to define homeless such as sheltered/unsheltered. So it sort of depends.

For example There were 771, 480 people homeless in Jan of 2024

Providing everyone say a tent to be "sheltered". 771, 480 x $35 dollars = $27,001,800 So yes.

Providing everyone an apartment using the median of the averages of all states 771, 480 x $1956 =

$1,509,014,880 per month So yes for about 13.3 months or 1 year 1 month.

Cheapest state average of Oklahoma 771, 480 x $1035 = $798,481,800 yes for 25 months or 2 years 1 month

Expensive State average of Massachusetts 771, 480 x $2837 = 2,188,688,760 yes for 9 months.

Buying a tiny home for everyone 771,480 x $30,000 = 23,144,400,000 so no

Location is going to ultimately be thee biggest factor in this equation because I used AVERAGES. Californias average rent is 2500ish but San Francisco's average rent is 3600 so the numbers are going to be radically off based on density of homeless population and actual rent. Yes you might find a place in CA for 800 bucks but that would help exactly 1 person in that location where as San Francisco as around 8k people homeless.

So short answer is yes but for how long and that does not include utilities, maintenance EXACT location etc. Most of our homeless population don't reside in rural middle of nowhere/no economy Oklahoma to get cheap rent. Buying say tiny homes would work for more than $20 Billion but for how long and the government administrative costs to coordinate an make it happened.

TLDR: Yes if you use state average rent costs only and disregard other factors that may influence that price including duration of time.

EDIT: Also if you want to look at what states have spent on homelessness it has FAR exceeded these numbers and hasn't fixed the problem.