Yes......maybe......it depends.....
What, exactly, is the "recommended tire size"??
If you run less than a 225 tire size on a 15" rim AND there isn't more than 1" of additional "dish" on the rims, AND the 4-bolt to 5-bolt spacer is less than 1-1/8" thick, it should fit.
HOWEVER!! I don't know what the dish spacing of your rim is, so "it depends".
Take off a wheel and measure from the wheel mounting flange on the hub to a vertical line dropped from the inside of the top of the wheel well lip on the fender. THAT is how much horizontal space you have to deal with.
Now, measure from the inside of the wheel center flange (that surface which mates to the hub flange) to the outside lip of the wheel. Add 1" to 1-1/2" for the sidewall of the tire and THAT is the max outside distance the tire will take up. Subtract that measurement from the max measurement for the wheel well you found in the previous step. The difference, minus 1/2", is the maximum thickness allowable for the lug bolt converter to make everything fit.
OK?
There are a bunch of variables here, so you really have to sit down and do the measurements and maybe even mock things up a few times before you arrive at something that looks "right".
As an example, I have 16" diameter by 6" wide rims with a 3.75" "dish" and I'm running spacer/adapters which are 1-1/8" thick (and 205 tire size on the front). Sometimes when I look at the front it looks just fine, and other times I wish I had another 1/2" of wheel (or 1/2" more of spacer) for a tighter look. Then I come to my senses and just have another beer.
gn