I have a #1 which gives so-so accuracy with any number of handloads. Good enough for most hunting, I guess.
The forend is clearly not free floated. Do #1's usually see accuracy improvement if floated?

Each model and cartridge can react differently. There are more ways to tune a #1 than Obama has lies.If it's a big game rifle and will put 3 in 1.5", it will kill anything you want to shoot at.
Try a google of Ruger No 1 accuracy tuning, you'll get about 190,000 hits. Problem is "method a" may work great on "rifle a" and be a disaster on "rifle b".

Free floating any rifle usually doesn't hurt but otherwise avoid any changes that cannot be undone.

Model ? Cartridge ? Good luck.

My person opinion is that some rifle barrels give better accuracy after a certain number of rounds. Whether this is because the rifle settles into its bedding or the barrel smooths out inside I don't know. I have had several rifles that started shooting better after 1,000 rds. My Ruger #1 in 220 Swift just fired its best group ever yesterday, 5/8" at 100 yds. and it has 3,000 rounds down the barrel.
YMMV
whelennut

it has on everyone that i have owned. I believe i have owned six over the last few years

I bought 4 different Ruger #1 rifles, trying to find one that did not shoot well, that I could use to re barrel.

But the one I found, a 270, waited for a year to get rebarreled, and then I did the super Copper clean out of the bore.
Now I just had time to shoot one group:
0.44" 3 shot group at 50y
But I can tell, it is too good to take the barrel off.

I am zero for four with Ruger number ones (22 hornet, 223, and 2-22 PPC). Mine were not accurate, or wouldnt hold zero or both.
Beautiful guns to look at, but that's it for me

In my experience, Number Ones do not respond well to free floating. Six to eight pound of pressure at the tip has always worked best for me. GD

Any experience with installing and using the Hicks Accurizer on #1s?

I bought a #1 RSI in 270 win a month or 2 back. Started shooting it with 130 gr factory Win PP ammo. It grouped them very well, 1 1/4 - 1 1/2 @ 100 yds. BUT.....The groups wandered over 3" horizontaly. That was allowing the barrel to cool between groups.
I free floated it as it had a lot of contact on both sides, and resealed the channel. Now it is an honest 1" gun with the same factory ammo. However If the barrel is not allowed to cool between each shot the group with string verticaly each shot. I fired 4 shots and they each climbed strait up about 3/8" per shot. I allowed the barrel to cool down a bit. The 5th shot was at the same elevation as the 3rd, and the last shot fired with a cold barrel was on top of the 1st.
I can live with that. Starting to hand load and hope to improve it a bit more.

I have an early (1980 or so) #1, in 7x57. It would not shoot consistent groups until i relieved the wood at forend tip- Now it usually shoots into 1 1/4" at 100... John Barsness has written there were some sketchy barrels on Rugers for a while. I may have one of those, and got lucky with my 'solution'
Interested in trying the Hicks device...

Of the three I have owned floating helped all three. Still have two; a .270 Weatherby Mag. and a 6mm Rem. The 7mm Mag went down the road.