Is it appropriate for a junior employee to request business cards prior to attending a conference? Is there some "industry standard" level or title that justifies business cards?
This really shouldn't have anything to do with how "junior" the employee is or this person's pecking order in the organizational hierarchy.
Instead, the question that needs to be asked is: Does this person actually need business cards? For a junior employee who doesn't meet with clients, who doesn't meet with vendors, and whose job role doesn't typically involve leaving the confines of the office, having a business card may not be a good investment in time and/or money, since there is no need.
However, if the person is attending a conference, this presents a huge opportunity to do some networking with potential clients and potential vendors. This junior employee may meet a potentially valuable client, someone who is interested in the services that the junior employee's employer provides. In this case, it would be in the company's best interests to provide the employee with the tools he or she needs to represent the business and provide a good first impression.
It would seem awkward if the junior employee says to his contact, "Hold on! I'll get my boss's business card. Don't leave!", as he runs to find his boss and retrieve her business card.
If you want business cards, just ask, whether you're going to a conference or not. (I like having them just to give to friends and family, or even to use as bookmarks.) They don't cost much, and the worst your employer can do is say no.
(Well, that's not the worst they can do, but if there are negative consequences for just asking for business cards, you've got other problems.)