(LSJ) Summoning and CrimethInc.

[suoli]

Can CrimethInc. be played after using The Summoning to recruit Grey
Thorne or some other ally that requires an anarch?

CrimethInc.
Type: Action Modifier
Requires: anarch Protean/Quietus/Thaumaturgy
Requires an anarch. Play after resolving a successful action that
requires an anarch or makes this vampire an anarch.
[pro] Untap this anarch.
[qui] Untap another ready anarch.
[tha] Put this card in play. During your minion phase, you may burn a
pool to untap a ready anarch you control.

Summoning, The
Type: Action
Requires: Presence
+1 stealth action.
[pre] Search your library for an ally or retainer. Show it to all
players and put it in your hand (shuffle and discard afterward).
[PRE] Search your library for an ally. This vampire recruits that ally
(requirements and cost apply as normal). Shuffle afterward.

Thanks in advance.

[floppyzedolfin]

I don't think so. The Summoning is not an action that requires an
Anarch. The fact that you retrieve something requiring an Anarch
doesn't turn it into an action that requires an Anarch.

[LSJ]

Correct