In the presence of an exception/throwable, is it possible to parameterize a logging statement?

Yes, as of SLF4J 1.6.0, but not in previous versions. The SLF4J API supports parametrization in the presence of an exception, assuming the exception is the last parameter. Thus,

String s = "Hello world";
try {
  Integer i = Integer.valueOf(s);
} catch (NumberFormatException e) {
  logger.error("Failed to format {}", s, e);
}

will print the NumberFormatException with its stack trace as expected. The java compiler will invoke the error method taking a String and two Object arguments. SLF4J, in accordance with the programmer's most probable intention, will interpret NumberFormatException instance as a throwable instead of an unused Object parameter. In SLF4J versions prior to 1.6.0, the NumberFormatException instance was simply ignored.

If the exception is not the last argument, it will be treated as a plain object and its stack trace will NOT be printed. However, such situations should not occur in practice.