Yes it will. I went for the DeWalt DCD785 a couple of years ago, I think the DCD795 is the newest version of that range which comes with a brushless motor and should be in budget or theareabouts. I think you will struggle to get the DCD995 in budget unless you do some selective importing from the US.
Once you have a battery and charger, units themselves are quite cheap - I have a DeWalt impact driver from the same range and it really speeds things up.
Speaking of DeWalt, I have just hit the button on the DCS355 Multi Tool. Can't wait for it to arrive!