Something like that. There are a lot of ways to tamper with this: participation is voluntary, of course, so if a patient would 'benefit' from being randomized to the 'right' arm, you'd encourage them to do it, while if they weren't, you'd encourage them to drop out (and maybe get the tested treatment themselves!). You'd filter the list in the first place, or use alternative names (My legal first name starts with one letter but I always go by a version of my middle name which starts with a different letter: which version does the doctor write down?). And so on.

One interesting example, from a retrospective:

It took only a few months to accumulate the required experience in the two hospitals (Reese et al. 1952). Allocation to ACTH or no ACTH was decided by drawing marbles from a jar containing an equal number of white and blue marbles: one morning, when a new infant became eligible for enrollment, I noticed that our head nurse shook the jar vigorously, turned her head away, pulled a marble out (just as she had been instructed); but because she didn't like the 'assignment', she put the marble back, shook the jar again, and pulled out the color that agreed with her bias! The importance of Bradford Hill's precaution in Britain's famous streptomycin trial to conceal the order of assignment in sealed envelopes was immediately obvious!