Great pictures.
Short answer:
Yes, a rip saw will cut turns. As with any saw, how fast it turns is mostly a matter of width of kerf in relation to width of the blade.
Long answer:
The “residential grade” band saw blades I am familiar with are all ground as rip saws. These are general purpose wood cutting blades, not re-sawing blades. Such blades are set up for turning, so they have a lot of set relative to the thickness of the metal of the blade, and they also have a fairly small blade width. For example, the 3/8 inch blade I’m currently running has approximately .01 metal thickness, and approximately .025 inch thickness as measured in the set. That 1:2.5 body-to-kerf ratio means it cuts a pretty wide kerf in relation to the width of the back of the blade. And with only 3/8 of blade width, it turns fairly easily in that kerf. I assume that that kind of ratio is pretty typical for a general purpose blade. It yields standard turn radii such as the following. (This is just a standard chart, available in half a dozen places on the web and on the back of every Delta band saw blade packaging.)
Blade width -- minimum cut radius
1 inch -- 7 inch
3/4 inch -- 5 1/2 inch
1/2 inch -- 2 1/2 inch
3/8 inch -- 1 3/8 inch
1/4 inch -- 5/8 inch
3/16 inch -- 5/16 inch
1/8 inch -- 3/16 inch
In contrast, a rip saw that has been set up for using as a hand tool is not likely to have the same ratios. Such a tool will have been designed just for making a straight cut, rather than for turning a radius. It is most likely going to have a blade body of thicker material than you find on a most modern band saw blades, and it is likely to have a body to kerf ratio something like 1:1.6, rather than the 1:2.5 mentioned above. What that means is that it is set up to run straight, and so it may only turn on a very large radius. But that’s just talking general principles. Without a having a lot more info, it’s hard to predict what the minimum radius of cut will be for the rip saw blade you are asking about.
It is possible to reduce the minimum radius of cut by grinding down the width of the blade. But again, there is no need (and no advantage) to grinding it down beyond what is necessary for the minimum radius you intend to cut.
It is also possible to reduce the minimum radius of cut by adding set to the teeth, thus increasing the width of the kerf. Of course, if you go that route, you are also getting into a more serious version of the saw sharpening game.
In general, you want to leave the blade as wide as possible (but strike a balance, so as to avoid loosing too much to friction and getting into hassles with binding, etc.). There are several reasons for this, and some are especially important for a hand tool.
(1) A wider blade generally provides a smoother cut. That’s because the back of the blade trails along behind as the teeth make the cut, and that trailing body basically acts as a long straight rudder, keeping the teeth pointed straight ahead. The more narrow the blade, the shorter that rudder. Accordingly, when sawing any line or radius greater than the minimum radius, the blade can have a tendency to wander back and forth. And that creates an irregular line, rather than a smooth cut.
(2) A wide blade simply provides more material, and thus more strength. In general, a wide blade can be stretched tighter than a narrow blade. A blade that is stretched tight is not as likely to follow the grain of the wood. And it is also easier to make a correction in direction with a blade that is stretched very tight. A loose blade is more likely to follow the path of least resistance through the grain, and it can be difficult to pull it back on line without bending and breaking it in the process.
(3) A wide blade provides more material for sharpening. I own a couple of antique bow saws and a felloe saw. The blades on those saws show themselves to have been sharpened many, many times. One has been sharpened so many times as to have lost about 1/3 of its original width (as estimated by the width at the pin holes). A slightly dull band saw blade will still cut, provided you are don’t feed it too quickly and it has a large enough motor pushing it! But a dull bow saw or felloe saw will be an absolute pain to use. It is only reasonable to use if it is kept razor sharp. The old carpenters knew this.
The radius of cut you need for the area under the lock of a long rifle will vary according to the style. An early VA rifle I’m working on now has a radius under the lock of around 12 inches. An Isaac Haines I have as a radius under the lock of around 10 inches. Would your rip saw make a turn with a 10 inch radius with the blade at 1 ½ inch width as it is right now? No way to guess. Would it make a tighter turn after being ground down to 1 inch, or ½ inch as you suggested? Certainly. But it seems to me that there is no good reason to grind it down without first testing it out to see what it can do as is.