Well, depends. Normal throws in this game have 3 frames of start-up. You can punish Kyo for doing Shiki-Kai as long as he does a move that’s not 2 frames or faster (Or something odd like his EX DP, but that’s different). If someone like Terry or K’ can’t hit her with a d.B, that means it’s probably -2 or 3 frames of recovery. If you got thrown, that’s probably the case.
What you can do with Athena to test this theory is set your dummy to do phoenix arrow into dp. You block it and then try to throw her. If she DPs you, that means it’s -2. If she can’t DP you and she gets thrown, it’s -3. Reason being is her DP is 4 frames of start-up (If it didn’t get faster than in arcade, which I doubt). If it’s -3 recovery, the opponent has 1 frame of wiggle room to grab you before he gets DPed. If it’s -2, you’ll go into your start-up animation for your DP which puts you in the air and unable to be grabbed.
Give it a shot!
EDIT: So I tried it myself. I can grab her the second she lands, but I can’t hit her with st.C or d.B with Terry, which I know has 4 frames of start-up. So, I’m fairly certain it’s -3 on recovery. That’s not good or bad, really. For most people, they won’t be able to poke you out of it. You can also TK it really close off the ground for a poke. Even if it’s -3, that just means it’s throwable. The window to throw Athena is kinda wonky because the time she lands is covered in pink sparkles. Unless someone has some knowledge of when they can throw, they won’t really know to throw you. Even then, you now know the only thing that can stop you are 1-3 frame command grabs, throws, and moves so you’ll know not to throw it out against people like Daimon, Maxima, Benimaru, Clark, etc, but also that if you mash a C DP, block and hold back C, or backdash, you could catch them 
Play with it a little. I hope to see you bring more ideas for your characters to the table!
EDIT EDIT: It doesn’t combo, but because it’s a pretty safe move with a very odd timing, you can make people scared to press buttons and do some sort of mix up. For example, you can’t combo B Phoenix Arrow, but the recovery’s so short that you can teleport or do her command grab if someone’s afraid to poke you. You could land and throw out a CD, cancel it, and throw a fireball to keep pressuring your opponent. Since it’s -3, you can also teleport and gain some distance for hit and run tactics. Use your imagination!