No 1600 model has a native DSL interface. If you have a 1605 model with two Ethernet interfaces, you could use one Ethernet to connect to a DSL device from the provider and the other Ethernet to connect to the office network. If you do not have 1605s I do not think you could make it work with DSL.
It looks from the product literature that there is a feature set for the 1605 that does support IPSec VPNs. That feature set requires 4 MB of flash and 12 MB of RAM.
To implement this you would need to get a public IP address from the ISP for each of the remote offices (and you need a public IP for the central site).
I have worked on a project at a customer site where we have implemented IPSec VPNs to connect remote sites to the central site (currently supporting about 80 remotes). Some aspects of the configuration can be a bit complex. If you are quite new to Cisco routing you may find this to be a challenging task. Best of luck.
HTH
Rick
HTH
Rick