Yes of course.It absolutely adds hardness It is exactly how magically my pure lead turns into 20-1 /16-1 hardness , from a BHN of 6 to a BHN of 10 according to my Cabin tree BHN hardness tester by adding tin into pure at the above ratios ! And not for nothing if I want harder I can bump the hardness to 20-22 BHN by doing nothing more to the above alloy than water quenching . I've done it for many(MANY YEARS) a necessary requirement of rolling your own PP 530 grain Rockets for long range for my TC Renegade 1-18 twist Rice barreled launcher
Adding tin to lead or lead alloys increases hardness and strength, but lead-tin alloys are more commonly used for their good melting, casting, and wetting properties, as in type metals and solders.
In bullet casting antimony is the primary hardening alloy. Tin is added for the reason mentioned above.