The AL players guide lists eligible +1 sources. You can choose the Elemental Evil Players Companion. I'm not sure if that is exactly the same as the elemental evil book you are referring to but I think it should contain the PC usable content from EE. Some of the EE content though was reprinted in XGTE so you might want to check that XGTE might not be a better +1 for your purposes. Also, if you are looking for backgrounds, they can come from any listed source and do no limit your +1.
"Step 1: Choose a Race and Class Forgotten Realms characters can choose race and class options from the Player’s Handbook and one other resource—a rule called “PHB+1.” Additional resources include the following products: • Elemental Evil Player’s Companion (EEPC) • Sword Coast Adventurer’s Guide (SCAG) • Volo’s Guide to Monsters (VGM) • Xanathar’s Guide to Everything (XGE)1 • Mordenkainen’s Tome of Foes (ToF)2 • Locathah Rising (LR)"
"Background. Choose or create a background using the Player’s Handbook or other campaign resources. Additional resources are permitted in the Adventurers League Content Catalogue (ALCC)."
can I use the elementals evil book as my phb +1
The AL players guide lists eligible +1 sources. You can choose the Elemental Evil Players Companion. I'm not sure if that is exactly the same as the elemental evil book you are referring to but I think it should contain the PC usable content from EE. Some of the EE content though was reprinted in XGTE so you might want to check that XGTE might not be a better +1 for your purposes. Also, if you are looking for backgrounds, they can come from any listed source and do no limit your +1.
"Step 1: Choose a Race and Class
Forgotten Realms characters can choose race and class options from the Player’s Handbook and one other resource—a rule called “PHB+1.” Additional resources include the following products:
• Elemental Evil Player’s Companion (EEPC)
• Sword Coast Adventurer’s Guide (SCAG)
• Volo’s Guide to Monsters (VGM)
• Xanathar’s Guide to Everything (XGE)1
• Mordenkainen’s Tome of Foes (ToF)2
• Locathah Rising (LR)"
"Background. Choose or create a background using the Player’s Handbook or other campaign resources. Additional resources are permitted in the Adventurers League Content Catalogue (ALCC)."
Thanks(and yes I meant EEPC)