Kind of blah, but I can't think of a ready-made saying. If it's not a diploma or is supposed to be more general, then substitute "piece of paper" and "paper" for the parts in brackets.

If, however, it's definitely a diploma and were, by any chance, intended to be more sarcastic, then the possibilities for fun would be many. So here are some likely irrelevant flights of fancy:

Without a diploma you're cooked; with a diploma - good luck!

(If you were Victoria Nuland you would say that with a much better rhyme in place of "cooked".)

Or this way:

Without a diploma you're at a dead end; with a diploma you're at a debt end!

or you need paper or a piece of paper

You won't go far in life without documents but if you have the 'right' documents you can make a name for yourself.

make a name for yourself = succeed in life, be a real success

'right' documents in single quotations because some elusive, hard-to-get documents that you need to jump through hoops to get were deemed more important and status-worthy

.

Попробую рискнуть и предложить свой вариант перевода этого забавного и в то же время житейского изречения применительно к российской действительности, хотя и других странах человек без документов вряд ли долго протянет.
Еще один более длинный вариант:
Chances are you would be out of trouble, if you've got papers at hand to make your point instead of soap bubbles.

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Note added at 5 days (2014-02-20 23:18:54 GMT)
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Для созвучия: troubles - bubbles.

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Note added at 5 days (2014-02-21 15:04:54 GMT)
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Все-таки evidence в моем переводе лучше, чем papers, хотя и выражает смысл размыто. Кроме того, papers точнее, чем просто a piece of paper, так как речь идет не о любой бумажке (или клочке бумаги), а о документах, которые нужно иметь при себе и без которых решение каких-либо житейских вопросов оказывается затруднительным. Your papers are official documents, for example your passport or identity card, which prove who you are or which give you official permission to do something. В связи с этим попробую предложить другой вариант: It's papers that matter if you face a situation when nobody cares about your frustration.