Depends on whether or not you're using JSF with Seam and what performance optimizations you use (like @BypassInterceptors, Hibernate 2nd level cache, etc.) as well as architecture/layering of your app.
Read the online Spring integration chapter (it's free) here: http://manning.com/dallen/SeamIACH15_bonus.pdf from SiA book. IMO, you're looking for trouble b/c these two frameworks are both very complicated and the integration process was somewhat complicated (also depends on which app server you're using).
One of the main reasons to use Spring with Seam is if you have an existing Spring app and you want to re-use the Spring beans and add the functionality that Seam offers. Perhaps also if you're interested in using AOP. Also, Spring offers JdbcTemplate but there is no equivalent of that in Seam. The @Transactional annotation is more robust in Spring than Seam. I'm pretty sure that Spring Web Flow offers some kind of conversation modeling/support but most likely not jBPM integration with JBoss AS which Seam does.
It seams that Spring has implemented the conversation and nested conversation concepts as flows and sub-flows:
Here's an excerpt from SiA ch15:
Which classes of Spring can be assimilated into Seam? Well, it depends on their
POJO rating, of course! As long as the class can act as a regular object, meaning it
doesn’t attempt to call out to the Spring container or depend on any Spring container
magic (at least that we can’t emulate), it’s a viable candidate. Here’s a small sampling
just to get you thinking:
■ Custom—Classes in your application being used as Spring beans
■ Lightweight remoting—HttpInvoker, Hessian, Burlap, and POJO
■ JDBC—JdbcTemplate and SimpleJdbcTemplate
■ iBatis—SqlMapClientFactoryBean and SqlMapClientTemplate