can I trust that a proportional/equal number of people are assigned to each condition
There are different settings available in the random generator how the randomization should work.
The default is to count the cases upon drawing. That means: If 120 people reach the page with the random generator, 30 will be sent to each of the 4 condition. If 20 drop-out in one of the conditions, that group will be smaller in the end.
The mechanism works like this: The random generator has a counter (visible in the random generator on the right), and it will take one of those codes that have the smallest count.
Another option is to tell the random generator no to count when the code is drawn, but when the questionnaire is finished (FINISHED=1). Sound nice, and work fine - but there are two drawbacks: First, that will create groups of different size when a large number of respondents starts at the same time. Because it has to draw before all have reached the end. And second, respondents leaving the questionnaire earlier (e.g., not answering an open-ended "any comments" before the last page) won't count.
There are also further mechanisms. Yet, I usually recommend the default setting.