A MoDaCo forums member has built a custom ROM for the HTC Touch HD that comes with Internet Explorer 6 preloaded. In other words, it's possible to get the browser running on existing hardware. Custom RUU - ensure you have HardSPL installed from here first! You can also install by extracting the EXE with WinRAR (PC) / Betterzip (MAC), renaming ruu_signed.nbh to BLACIMG.NBH, placing it in the root of your storage card then turning on your device with the volume button held down.
If you’re concerned of voiding-warranty, you can try Opera Mobile, , which is entirely legal and has the added benefit of supporting tabbed browsing.