Yes, you can do that with a pigment printer. When I hear people talking about using a WF1100, I immediately assume dye sub work as that's what a lot of people are using them for.
Most people refer to "heatpress stuff" as "T-shirt transfers", vs. dye-sublimation or heat pressed vinyl, which are also technically "heatpress stuff".
If you're looking to print on vinyl, then you'll be very limited in options using a desktop inkjet printer - there is a limited selection of vinyls that accept aqueous inks.
You'll definitely want to go with pigment inks for t-shirt transfers or for printing vinyl.
I purchased my WF1100 from a forum member. It came with refillable cartridges and a large supply of high temp inks - so much so that they went bad before I could use them all up. I recently purchased a generic CISS off of ebay and filled it with fresh Cobra Ink high temp inks and it's made a world of difference in final color output, and it's so much easier than using a syringe to refill those old cartridges...
You can buy a brand new WF7010 for around $200, a generic CISS for it will run you about $40 on ebay and then you can get the inks from Cobra Ink (four 4 oz bottles is $51.99) to fill it up yourself. Or you can buy the whole kit and kaboodle (printer, CISS and pigment inks) directly from Cobra Ink for $359. They no longer pre-install the CISS kit, but they will walk you through the process and provide phenomenal support if you need it. I would love to see a 13"x19" version of the WF4020 - it has internal, re-fillable 4 oz. ink cartridges and so no need for a CISS kit. I love my WF4020 - would love it more if it could do up to 13"x19"...