Are 1903 susceptible to headspace issues with the multiswap non-serial bolts?
Would a set of go/no go gauges be prudent for any 1903 investigation?
A go gauge is generally not helpful if the barrel is already on it. Go gauges are used to make sure that the rifle has the minimum headspace to operate when the barrel and bolt are assembled into a rifle. A snap cap or dummy round set to maximum OAL will suffice usually to tell if the barrel-bolt combo headspace is too short. Do not use live cartridges for this action unless perhaps you are on the range pointing the rifle in a safe direction, etc.
While too short headspace could be an issue, it usually is not in a used military rifle, bolt, and barrel. On commercial sporting rifles, you sometimes will run into a rifle that does not accept the maximum OAL for a cartridge sometimes due to differences in the chamber area. Using a dummy round and gently trying the bolt usually indicates this situation. If you want to do it in the store, a snap cap is the preferred way as retailers can tell that the round is not live. If the bolt, barrel, or both, have been substituted for a new ones, it is possible to have too short headspace.
Now, we enter the no-go gauge use. The no-go gauge sets the maximum allowable headspace for a new rifle barrel-bolt relationship and also allows a check of an older rifle to determine if the headspace has increased beyond a set maximum by the std. bodies that provide specifications for ammunition such as CIP or SAAMI. There is also a field gauge that indicates the maximum headspace on a used rifle which is set a certain distance beyond the no-go gauge. On old military rifles and some civilian antique rifles, field gauges are often used because chambers were generous, many old military cartridges and chambers were made before standardization bodies existed. Also, headspace means something very different on rimmed or straight cartridges, and so on.
On sporting rifles, or match type rifles, many folks change their barrels when they reach the no-go range because of brass life and sporters may not handle escaping gas from a cartridge separation particularly well. There is a relationship between excess headspace and accuracy but that relationship is too complicated to explain and individual rifles differ in effects. Generally excessive headspace is believed to make rifles less accurate more or less.
Depending on the design of the rifle, too long headspace has different consequences that are too much to summarize in a post. However, the basic risks are that of the brass in the cartridge being stretched so much that it releases hot gas into the receiver rather than the barrel, the primer being driven out of the pocket tying up the rifle, and perhaps introducing hot gas around the firing pin hole. Worse effects include bolt recess setback as the bolt becomes a sliding hammer on the receiver lug recesses due to play in the bolt, and ultimately bad things like grenading the receiver, shearing off bolt lugs, and so on depending on how bad the headspace issue is. It is one of those unpredictable things based on individual factors involving the cartridge brass, the strength of the receiver and bolt, gas handling, the pressure load of the ammo, the condition of the rifle, whether or not a magazine exists, and so on. The effects are unpredictable and thus constitute a danger to the shooter.
Mild cases where the rifle is between the no-go and field specs have been addressed by either only using new brass and/or ammo and knowing that any fired brass should be carefully inspected for stretching and incipient cartridge separation, using fireformed brass made in that rifle as if you made a wildcat, or using light handloads like safety would dictate for any dubious firearm. It can also be addressed in some rifles, particularly Mausers, by requalifying the barrel which involves lathe and rechambering. Timed and coned barrels like the U.S. used, it can be very complicated and hence expensive to rectify this way in order to keep the historic barrel with the receiver.
Summary, a no-go gauge can be helpful as can a field gauge if you do not mind the tradeoff. Go gauges are most helpful if you are testing a new rifle or you have had bolt/barrel work where the bolt/barrel relationship has changed via a new barrel, bolt, or both. If you assemble AR's a go gauge can be helpful as tolerance stacking can result in too short headspace. If you buy the bolt and barrel from the same place, you can specify at some retailers that you get a bolt and barrel that qualify in headspace. Be aware that headspace means something different between a bottle neck cartridge, a straight cartridge that headspaces on the mouth, or a rimmed cartridge.