Bottom line:  There is some lower level evidence that remifentanil may be associated with a lower seizure threshold.

Search methods:  Searched EMBASE and Medline using these concepts:
remifentanil AND electroconvulsive therapy
Applied filters for RCT and systematic reviews

Search results:
REVIEWS OF EVIDENCE:
Remifentanil: A review of its use in electroconvulsive therapy
Chen S.T.
Journal of ECT 2011 27:4 (323-327)
Review includes study (Sullivan et al.) that documented effect of remifentanil on seizure threshold (lowered threshold and results in lower rise in threshold than comparison group.)  This was a very small (n=24) retrospective study.

Effects of general anesthetic agents in adults receiving electroconvulsive therapy: A systematic review
Hooten W.M. and Rasmussen K.G.
Journal of ECT 2008 24:3 (208-223)

RCTS:
Effects of remifentanil on convulsion duration and hemodynamic responses during electroconvulsive therapy: A double-blind, randomized clinical trial
Nasseri K., Arasteh M.T., Maroufi A. and Shami S.
Journal of ECT 2009 25:3 (170-173)

Propofol versus propofol-remifentanil combination anaesthesia in electroconvulsive therapy: Effects on seizure duration and hemodynamics
Algül A., Şen H., Ateş M.A., Yen T., Özkan S., Durmaz O., Erbinç S., Daǧli G. and Çetin M.
Klinik Psikofarmakoloji Bulteni 2009 19:SUPPL. 1 (S153-S154)

Remifentanil supplementation of propofol during electroconvulsive therapy: Effect on seizure duration and cardiovascular stability
Vishne T., Aronov S., Amiaz R., Etchin A. and Grunhaus L.
Journal of ECT 2005 21:4 (235-238)

Effects of remifentanil and alfentanil on seizure duration, stimulus amplitudes and recovery parameters during ECT
Akcaboy Z.N., Akcaboy E.Y., Yigitbasi B., Bayam G., Dikmen B., Gocus N. and Dilbaz N.
Acta Anaesthesiologica Scandinavica 2005 49:8 (1068-1071)

Seizure duration with remifentanil/methohexital vs. methohexital alone in middle-aged patients undergoing electroconvulsive therapy
Smith D.L., Angst M.S., Brock-Utne J.G. and DeBattista C.
Acta Anaesthesiologica Scandinavica 2003 47:9 (1064-1066)

The effect of remifentanil on seizure duration and acute hemodynamic responses to electroconvulsive therapy
Recart A., Rawal S., White P.F., Byerly S. and Thornton L.
Anesthesia and Analgesia 2003 96:4 (1047-1050)