Can stainless steel swords be used as weapons? Yes and no. Even though many replica swords - especially replica katanas - have a sharp edge and can be used to cut, this does not make such a sword a reliable weapon, as any sharpened length of metal can do the same!

There are serveral issues one must take into account when considering a stainless steel replica sword as a personal weapon:

(Many thanks to Motoyasu for providing excellent technical information on Japanese swords!)

Safety

A stainless blade is much weaker than a comparable blade of plain carbon steel would be. Also, the materials of replica swords tend to be substandard because they were made at low cost, e.g. plastic or scrap softwood hilts, badly fitted, very short partial tangs, loose fittings, etc.. Thus, all of these factors can represent a source of possible failure and a safety hazard to you or anyone around you. It may not happen today or even for years, but if you ask around the dojos (martial arts practice centers), you'll find that breakage of these swords has occured with frightening regularity - some were hilt failures, others were blade failures, none (so far, fortunately) have been fatal. But do you want to take that chance?

Cutting Ability

Replica swords were meant for display and not for actual use, so they have many deficiencies in terms of geometry, curvature, weight, balance. This is most certainly the case with replica Japanese swords!

With replica Japanese swords, the "razor sharp edge" these swords most often come with (especially Taiwanese made swords) actually contribute a great deal to cutting resistance if compared with a real Japanese sword. These replic katanas are sharpened by grinding a bevel about 1/16" or so wide on the edge of the blade. Not only can this never be as sharp as a sword without the bevel, but even this minute little ridge contributes a great deal to cutting resistance.

At a more technical level, replica blades typically have flat sides. Sharpened in the way they are, replica swords may have a larger edge angle than real Japanese swords, but the shape of the blade means increased cutting resistance as the object being cut will touch the flat all the way through the cut, while with a real Japanese sword - where the sides are slightly convex - the object being cut would only contact a single point on the curved surface. The convex edge is also tougher than a flat-sided edge and resists chipping better! The narrower trailing edge in a real sword results in no contact with the object. The diamond cross section also increases rigidity of the blade, making it less likely to bend.

Curvature

Many replica Japanese swords do not have the proper amount of curvature. In some cases, the curvature occurs on the wrong place on the blade. Many wall-hanger swords, unfortunately , have a short, straight hilt which does not follow the curvature of the blade. All of these reasons can result in a blade being more likely to chop than cut. By design, a Japanese katana's true strength comes from its ability to cut, not as a chopping weapon. Thus, improper use such as chopping can result in bending or breaking a sword! Even if you do manage to perform a cut with a replica sword, because of the wrong sized hilt, you usually cannot generate sufficient power in the cut!

Weight & Balance

There are also issues with weight and balance. Most replicas are too heavy or too light, and their balance is either way too blade heavy or too far down towards the hilt, with obvious consequences for cutting and other use of the sword.

Durability

Replicas are generally made of substandard materials which means there were compromises in the physical quality of the sword. Because of this, replica blades usually end up not being able to hold an edge under use. If you sharpen it and leave it, the edge will be fine, but if you cut with it, after a few cuts, you will find that it has dulled already! Compare this to a real katana where you'll probably never have to resharpen it in your lifetime unless you chip it. The cheap fittings on replica swords will typically deteriorate and fall apart very quickly because they are just for appearance and not for use.

Conclusion

So in summary, while any sharp blade certainly can be used to cut with, the durability of such swords is an issue: the edge will not stand up to any abuse, the fittings and furniture may fall apart on you. Also, because the blade is intended for display, its shape, geometry and balance are not optimized for actual use. While this particular deficiency can to an extent be compensated for by good technique, the paramount concern should be safety- again, replica swords are meant for display, not for real use, so they typically use substandard materials that may break and cause injury. Replica swords should be used only for display purposes, any kind of use, even stage fighting, should be done using swords made for the purpose.