If both people genuinely enjoy golf, it can be a perfectly normal relationship-building setting. The activity itself is not a recruiting hack.
Do not manufacture a golf connection because you think senior consultants expect it. A shared interest works because the conversation becomes more natural, not because the sport carries special recruiting weight.
If you are invited, treat it like any other professional-social setting: be easy to spend time with, do not turn every hole into a recruiting question, and let the relationship develop normally.