Yes it does but you'll need to figure out the number of
expected routes to calculate the required memory
but a full memory capacity of the c3600 should be able to support BGP.
example of how to calculate your mem requirement for bgp.
say you have 100000 bgp routes coming from only
one neighbour. then the calculation is as below.
(a) number of prefixes (240 bytes per prefix)
(b) number of routes (240 bytes per route)
(c) number of alternate paths (110 bytes per alternate path)
BGP table : 100000 X 240 =24MB
routing table (bgp) 100000 X 240 =24MB
Alt. Paths : 100000 X 110 X N (n=0)=0
total memory requirement = 48MB/s. for 100000 bgp routes