No.  A small percentage of space is preallocated to prevent that.  However, if you do allot of writes, then TP volumes won't save you space in the long run.  
Hi all, Does equallogic Thin Provisioning affect performance? e.g. I created a Volume with thin provisioning enabled, but this Volume will be usef for heavy I/O application data, such as Oralce data. Thanks.  
about Equallogic PS SAN Thin Provisioning 