I tried to enable profiling on a secondary to see if I get distributed reads and seems to fail:

I ran:
mongo
MongoDB shell version: 1.8.0
connecting to: test
cloud1x:SECONDARY> db.setProfilingLevel(2)
{
"was" : 0,
"slowms" : 100,
"errmsg" : "exception: replSet error : logOp() but not primary?",
"code" : 13312,
"ok" : 0
}

And the log shows:

Assertion: 13312:replSet error : logOp() but not primary?
0x562059 0x7124a1 0x710362 0x77cf13 0x76a5a9 0x7dfd18 0x7dc5f0 0x7ddb21 0x645565 0x64addc 0x757f15 0x75a440 0x8a617e 0x8b92d0 0x7fe2026629ca 0x7fe201c1170d
/usr/bin/mongod(_ZN5mongo11msgassertedEiPKc+0x129) [0x562059]
/usr/bin/mongod() [0x7124a1]
/usr/bin/mongod(_ZN5mongo5logOpEPKcS1_RKNS_7BSONObjEPS2_Pb+0x42) [0x710362]
/usr/bin/mongod(_ZN5mongo12userCreateNSEPKcNS_7BSONObjERSsbPb+0x653) [0x77cf13]
/usr/bin/mongod(_ZN5mongo8Database17setProfilingLevelEiRSs+0x349) [0x76a5a9]
/usr/bin/mongod(_ZN5mongo10CmdProfile3runERKSsRNS_7BSONObjERSsRNS_14BSONObjBuilderEb+0x118) [0x7dfd18]
/usr/bin/mongod(_ZN5mongo11execCommandEPNS_7CommandERNS_6ClientEiPKcRNS_7BSONObjERNS_14BSONObjBuilderEb+0x9a0) [0x7dc5f0]
/usr/bin/mongod(_ZN5mongo12_runCommandsEPKcRNS_7BSONObjERNS_10BufBuilderERNS_14BSONObjBuilderEbi+0x831) [0x7ddb21]
/usr/bin/mongod(_ZN5mongo11runCommandsEPKcRNS_7BSONObjERNS_5CurOpERNS_10BufBuilderERNS_14BSONObjBuilderEbi+0x35) [0x645565]
/usr/bin/mongod(ZN5mongo8runQueryERNS_7MessageERNS_12QueryMessageERNS_5CurOpES1+0x31ac) [0x64addc]
/usr/bin/mongod() [0x757f15]
/usr/bin/mongod(_ZN5mongo16assembleResponseERNS_7MessageERNS_10DbResponseERKNS_8SockAddrE+0x5b0) [0x75a440]
/usr/bin/mongod(_ZN5mongo10connThreadEPNS_13MessagingPortE+0x21e) [0x8a617e]
/usr/bin/mongod(thread_proxy+0x80) [0x8b92d0]
/lib/libpthread.so.0(+0x69ca) [0x7fe2026629ca]
/lib/libc.so.6(clone+0x6d) [0x7fe201c1170d]