FPGA Memory vs Registers
The actual storage elements for registers and RAM in an FPGA are the same. What matters is the routing resources available. RAM can be thought of as a dedicated array of registers with with a relatively small number of signal lines controlling a whole lot of registers. This allows you to handle a lot of data without using a whole lot of interconnect resources, which are actually the limiting factor in FPGAs.

So the answer is, yes, you can use registers instead of RAM. And no, using 1024 of them is not a great idea since it is likely to suck up a lot of your FPGA, both in functional cells and in operating speed.

You're much better off figuring out how to use your RAM.