It’s complicated. The thickness is more critical than the exact size of glass. However, if the “spacer” between the panes does not align perfectly with the frame opening, you could see the spacer through the window or it could be recessed deep into the frame.
First, I’d measure the inside dimension of the “spacer” and see if it matches the existing. If it’s “off” it will be noticeable.
Second, I’d hold the new unit up next to the remaining unit (not the unit you’re removing) and see if it’s the same “color” as the existing. Some glass is tinted (for various reasons) and some has argon added. The damaged unit could turn a different color by releasing its argon gas.
If either of these things don’t match up perfectly, I’d have it replaced.
If the size and color are acceptable, then I’d check the thickness. There are several factors that will affect your installation: 1) thickness of glass, 2) thickness of spacer, and 3) thickness of “sealer tape” between the glass unit and the vinyl frame.
1) The thickness of the glass can affect the color, so it matches in color, it probably matches in glass thickness.
2) Often a glazer will change the thickness of the spacer if he doesn’t have the correct glass thickness.
3) The only other adjustment in thickness is the sealer tape. Because the unit is thicker than the original unit, you may be able to use a thinner (or softer) tape so the unit will fit in the frame. By the way, the glass unit is sealed to the INSIDE flange of the window. The stop is just used to hold the window unit tight to the “sealer tape”.
If all that works out and you decide to proceed, get some spacers to hold the glass unit in proper position until you can install the stops.
If the sash slides, it can be removed from the frame. I’d remove it and take it to a glass shop. They can replace the glass in about 15-20 minutes.
Take pictures of each step of how you removed the sash, because its tricky getting it back in the opening. I did my daughters, but I couldn’t get the wires/springs hooked back up, so now it’s a “fixed” window.