Siamese Algae Eaters will usually eat brush algae, but I'm not sure about staghorn or other types. But there is a much more important point to be made, especially as you don't want to add another fish. Please don't.
SAE have specific requirements. While many have just one, they are shoaling fish and should be in a group of six so they establish their hierarchy. Denying them something they expect is not advisable. Second, they get largish, six inches, and this will have a significant impact on the tank biology.
Another issue is that many different species appear under the common name of SAE, and some of these bring other problems with them.
Algae should always be dealt with by addressing the cause. In a planted tank this means finding the balance of light and nutrients sufficient for the plants but no more or less. In non-plant tanks, algae is not really a problem as it is merely performing some of the benefits of higher plants, but again light and nutrients are the cause, and without plants some forms of algae is inevitable.
Byron.