Structurally you'd be OK, but when it comes time to put up the interior-side gypsum you'd have a pretty thin strip to nail/screw to along the bottom plate.
In a 10 x 10' space you could install subfloor along just exterior walls initially, leaving just one sheet out for access rather than cutting.
In any new construction with a tiny crawlspace it's worth laying down a 6-10 mil vapor retarder over 6" of washed pea gravel, then insulating the crawlspace floor with a couple inches of EPS, and the interior side of the crawlspace walls with a couple of inches of foil-faced polyiso held in place with furring through-screwed to the foundation, air-sealing the band-joist and foundation sill with can-foam, with either cut'n'cobbled polyiso or R15 rock wool insulating the band joists. Tape the foil facer seams with FSK tape (2" foil duct tape), and use can-foam to seal the top & edges to the sill/floor-EPS. A 1"-2" rat-slab of concrete (or even half-inch OSB, if that's cheaper/quicker over the EPS is sufficient thermal barrier to meet code on the floor-foam, and adding R15 rock wool to the interior side of the wall-foam brings it up to code for thermal barrier there. In a 1-2' high crawl this is less insulation than doing the floor at a code-min R30, puts all of the plumbing inside the thermal boundary of the structure, and the floor will be much warmer to boot, since you won't have the cold stripes of thermal bridging of the joists to a super-cold crawlspace. A couple of floor grilles on opposite corners of the room is all that would be needed for ventilating a space that small, guaranteeing that moisture or gases don't build up in the crawl.
Code min wall in most of PA is 2x6 with R20 (or higher) in the cavites, but you get more performance at the same depth out of a 2x4 wall with 2" of EPS or iso outside the sheathing, under the siding and R13-R15 in the cavities. (R5 rigid foam sheathing on an R13 2x4 walls also meets code min, and is a more resiliant assembly than a 2x6/R20 wall.) No matter what wall type you build, it's worth caulking the framing to the structural sheathing inside each stud bay with acoustic sealant or can-foam to prevent outdoor air from convecting through the fiber insulation. If you go with cellulose or R15 rock wool the convection rates within the cavity are near-zero if you take the time to trim the fit perfectly (if batts), and split rather than compress around wiring/plumbing etc.
If you have at least R7.5 of exterior insulation on the exterior of a 2x4 wall you would not (and I'd argue should not) use an interior side vapor barrier in any PA location. In most of the state you could get away with R5, and in the warmer coastal area even less. An inch of polyiso is R6, two inches of EPS is R8, two inches of polyiso is R12-R13. A 2x4 wall with R15 batts and 2" of polyiso has a "whole-wall" R of about R23-R24 after factoring in the thermal bridging of the framing, whereas a code-min 2x6/R20 wall runs ~R13-R14 whole-wall, depending on stud spacing and siding type, the amount & size of window framing elements, etc.
If you go with the R23 wall and the high-R crawlspace, and keep the window area down to maybe a pair 15" x 30" transom windows over the washer & drier for daylighting you probably wouldn't even need to provide explicit heating to the room- just leave the door open (provided it's a door that closes and, not an open archway) during cold snaps.