Should I increase max_connections in AWS RDS t1-micro for MySQL?
Each connection carries the load of per-connection buffers as set by these parameters

join_buffer_size
sort_buffer_size
read_buffer_size
read_rnd buffer_size

Changing the number of connections increases the amount of memory each connection can demand to this : (join_buffer_size+sort_buffer_size+read_buffer_size
+read_rnd buffer_size) X max_connections
I have written about these before

Jan 03, 2012 : Understanding mysqltuner Recomendations w/ Unused Catalogs
Apr 24, 2012 : How costly is opening and closing of a DB connection?
Feb 01, 2013 : Show processlist / Max concurrent connections seem to max out at 131

ANALYSIS
Amazon has to set the number of connections based on each model's right to demand a certain amount of memory and connections
MODEL      max_connections innodb_buffer_pool_size
---------  --------------- -----------------------
t1.micro   34                326107136 (  311M)
m1-small   125              1179648000 ( 1125M,  1.097G)
m1-large   623              5882511360 ( 5610M,  5.479G)
m1-xlarge  1263            11922309120 (11370M, 11.103G)
m2-xlarge  1441            13605273600 (12975M, 12.671G)
m2-2xlarge 2900            27367833600 (26100M, 25.488G)
m2-4xlarge 5816            54892953600 (52350M, 51.123G)

I wrote about this as well : When should I think about upgrading our RDS MySQL instance based on memory usage?
This allows Amazon to do the following:

Charge you for each memory model based on seamless MySQL usage
Fairly Apportion Resources for MySQL RDS per region
Shoot yourself in the foot for tampering with per-connection settings

RECOMMENDATION
Perhaps you should try useing Amazon EC2 where you have no restrictions on access to my.cnf