Have the spelling systems of lingua francas historically been less phonetic than those of native languages?

Even a brief look down the list of Lingua Francas (http://en.wikipedia.org/wiki/List_of_lingua_francas) will show you that there is no tendency toward more opaque spelling systems.

But there are more fundamental misassumptions here that are worth pointing out.

1. Lingua Francas do not require to be written at all. They can be spoken or written or both.
2. Lingua Francas vary in how much their structures are impacted by their cross-communicative function. English for instance has not developed any notable structural features in its role as Lingua Franca.
3. Do not confuse Lingua Franca with concepts like Pidgin or Creole. While there are certain limited features that we can expect many Creoles to have in common, there is no such commonality with Lingua Francas. I suspect you will find certain commonalities in their use by non-native speakers due to imperfect learning but this may or may not have an impact on the language structure itself depending on context of use.
4. I wonder if the question may have been inspired by the case of Chinese where the orthography itself serves as a sort of Lingua Franca. Divorce between orthography and pronunciation is very useful for the many Chinese languages that use the characters without regard to pronunciation because the characters don't give any hints as to pronunciation. But this is not the case with English (or any non-pictographic system of orthography).
5. There's really no such thing as 'phonetic spelling'. It is much better to talk about opaque and transparent orthographies. The latter are more predictable but they will still adhere to some sort of an ideal representation (often linked to a standard) rather than represent speech directly. English is one of the more opaque systems but this in no way enables communication. It simply makes it harder to learn. Also, English has resisted long-standing efforts at spelling reform long before it became the Lingua Franca it is today.