No, putting anti-spam or security measures in place will not increase your attack surface. However, it could easily change your perception of this because you’re now seeing all the many attacks that your site is under on constant basis.
A good example is brute force protection for your admin login. Without that protection in place, as long as your password is strong, you’ll likely never notice anything at all.
But, as soon as activate protection, you’ll now see the logs for the constant onslaught of bots attacking your login, and locking it up, depending on your settings.
This massive shift in perception, despite the nature of things not actually ever changing, can and certainly does make people feel like they’re being targeted, especially by denial of service attacks.
In general, 99.9% of attackers aren’t targeting YOU specifically, rather, they’re attacking WordPress, who like Windows, is the best and easiest target.
That said, it’s always possible that you really are specifically under attack. Do you have any reason to believe so, and more importantly, did you already have these concerns before ever installing Stop Spammers?
Also, are you running your site through Cloudflare?