It will influence your relationship, positively.
Executives and managers always pay attention to these details and negotiate them when joining a company. The fact that you're paying attention signals that you actually understand what's going on and demands respect.
Some companies will refuse to give you this info and resent you for asking, but you should automatically reject such offers.
If a "rank and file" developer goes back and forth grilling them over offer terms, and is exceptionally picky above his peer group, this DOES make it back upstream in negative ways.
Some companies will not give you this as a matter of policy - , if you are ok with the salary, you could still enjoy working there - and may also make a great deal of money (or you might not).
Then don't work for those companies.
Ones goal in life should not be to get exploited at shitty startups as a "rank and file" developer (aka chump).
All being said, if at that stage of a job offer, you don't want to be looking like the most important thing to you are your options. If you get a decent salary and like the work, you are not being exploited.