A lot depends on what computer science courses you're talking about specifically, and what courses are included in your undergraduate degree already. I would expect most undergraduate physics programs to include at least one introductory computer science/programming course, and if you're hoping to go the theoretical route, you should probably pick up a numerical methods course in your junior or senior year if that's not already part of your curriculum.
On top of that, though, a lot can also depend on your level of independent experience. Some students take quite well to programming and once they know the basics are able to develop a strong skill set by embarking on their own projects independent of school. Others need that formal environment.
It's also worth considering too the fact that a career in academia is highly competitive - so much so that the odds are quite high you'll end up leaving it for a commercial job at some point. At that point having a documented set of computing and network administration skills will be quite useful in gaining employment.