Actually they might get about the same benefits, maybe less for those who are older due to old age.
Researchers found that young adults proficient in two languages performed better on attention tests and had better concentration than those who spoke only one language, irrespective of whether they had learned that second language during infancy, childhood or their teen years.
The study appears in the current edition of the journal Frontiers in Psychology, led by Dr. Thomas Bak, a lecturer at Edinburgh's School of Philosophy, Psychology and Language Sciences.
So the above proves that young adults that learned a second language from teens years and down (around 16- or 18-) can have positive effects such as better attention skills and more concentration than those who didn't through research.
Whether the positive effect extends to people who learn a language in middle age or beyond is not clear, but Bak and other brain researchers said they see no reason why not, and that is the focus of ongoing studies. "We have worked our way from adolescents to early adults," Bak told LiveScience. "We are currently working on middle age to retirement."
It is quite not sure about those who are older when they learn a language but it seems that the positive effects will still be there. From experience, my mom is learning English and is seeing/experiencing the effects in the above paragraph (not in yellow).
In the new study, bilingual young adults performed better in ignoring irrelevant stimuli and focusing on relevant information. One possible reason for this ability is that the very processes of learning two languages and switching back and forth between them train the brain to be more attuned to auditory information, Bak said.
This improvement in what is called auditory attention is essentially a measure of concentration, and could, for example, enable a person to better extract relevant information from a lecture, Bak said. He also noted that many drugs aimed at lessening the effects of Alzheimer's disease work by attempting to improve this attention mechanism.
Even more positive effects are shown here. Adults that learned another language seems to be more able to reject irrelevant information and only take in the necessary information. This is called auditory attention, which can allow people to extract more information from lectures and can help drugs trying to cure Alzheimer's disease as these drugs hope to raise this attention.
Source: Learning a New Language at Any Age Helps the Brain