The meat of the question: are actual stored procedures the only mechanism that implements temp table caching or do system stored procedures such as `sp_executeSQL` / `sp_execute` also take advantage of them?

I am not a DBA, so please use little words. Our application sends over prepared statements that, from the profiler, I see run all SQL through `sp_prepexec` which is a system procedure for both running `sp_prepare` and `sp_execute`. What I'm trying to do is figure out if I am benefiting from temp table caching. 

I've been using this guide with object_id() to examine behavior

https://sqlkiwi.blogspot.com/2012/08/temporary-tables-in-stored-procedures.html

Then point #3 on this blog post suggests that EXEC cannot use temp table caching, but leaves out whether sp_executeSQL can:
http://blogs.msdn.com/b/turgays/archive/2013/09/18/exec-vs-sp-executesql.aspx

In my query sent over via the client I have created a simple temp table.

    DECLARE @foo int; -- set by JDBC, unused but required to force a prepared statement

    SELECT 1 AS id
    	INTO #tmp
    
    SELECT OBJECT_ID('tempdb..#tmp');

In profiler, I can see:

    declare @p1 int
    set @p1=NULL
    exec sp_prepexec @p1 output,N'@P1 int',N'declare @foo INT = @P1 
    
    SELECT 1 as id
    	into #tmp
    
    select Object_id(''tempdb..#tmp'');
    DROP TABLE #tmp;',1
    select @p1

I also get a cachehit from this. However, the object_id of the temp table appears to be changing on me, which is not the behavior I would see if this temp table were created in a real stored procedure. However, when I run this same code through `sp_executeSQL`, I'm also seeing that the object_id of the temp table has changed. This leads me to believe that only "real" user created stored procedures take advantage of temp table caching.