You can do this in a manner of speaking. Place your parts then select the Place Line drawing tool at the top of the screen, select your board layer as the active layer and then draw the line between the pins your wish to connect.
This is definitely not the prefered method for doing this. It is preferable to have the nets as this could affect the ouput of the gerber files when it come to sending the board for manufacture. If you are doing your own boards then this may not be a problem. Also, there are features that require the nets like Connectivity Check, the aurorouter, Netlist and DRC Check, etc. Also you will get DRC errors in the spreadsheet when you do this as Ultiboard treats the pins not assigned to a net as unsued. It will say "Design Rule Error: Unused Pin Is Connected to Copper", but this can be filter out so that it doesn't pop up.
I would suggest reading about the Netlist Editor in the user manual and become familiar with the process of assigning nets to pins. It isn't that hard to do once you become familiar with it and this would open up the autorouter for you to use instead of manually placing traces. If you have Multisim in conjuction with Ultiboard then you have the ability to draw your schematic in Multisim and then transfer it to Ultiboard and this would automatically assign nets to your component pins. Your post didn't say if you had Multisim or not, but I thought I would pass this along in case you do have Multisim.
I hope I have helped some. If you need assistance with anything the forum is always open to any question you may have.
The only dumb question is one that is never asked. (I forget who actually made this quote, but it is a good one).