one mile vs. ten miles is a big difference!
The simple idea is that nobody can tell you definitively simply from the information on this post. How you determine this is by doing an RF link-budget analysis. I.e. What is the gain of the omni-directional antenna, link distance, fresnel zone clearance, terrain, receive antenna type, type of modulation used, and fade margin desired. Luckily most radio vendors have their proprietary link analysis calculators that allow you to plug in what the environment is, what type of antennas you are using (if the radio doesn't already have integrated antennas), link distance, and what reliability you need at what speed etc etc etc and they tell you if this is doable.
So in short you cannot answer this question generally.
But i agree with whoever told you that for such long range high speed links you almost always use high gain directional panels or dish antennas. So I like the suggestion to use 3 120 degree sectors instead of the omni. You may or may not need to have 3 separate radios.
Our primary partner with links at this distance is Proxim Wireless. Check out for example their Tsunami QB series point-to-point radios. Once you sign up as a partner they will provide their link budget tools for free and this will give you are very good idea on what radios and antenna configurations you can use.
So just to clarify whether an omni will work or not will depend on the RF link budget. You start with what the transmit power is which is determined by the radio you pick (pretty much limited by the FCC for the particular frequency band used), what the transmit antenna is (if an omni what the gain is which determines the EIRP - effective isotropic radiated power), then you determine what the path loss is (which depends on the link distance, type of terrain, type of environment e.g. rainy, dry, urban, canyons etc - the link calculator will figure out what the path loss is when you enter this), what the receive antenna gain is, and finally what the receiver sensitivity is (which depends on the radio - receiver sensitivity is the minimum amount of signal required - or SNR - to correctly receive signal with a certain modulation). Other factors come into play such as the modulation used, amount of error correction etc. But all these are radio specific and the link calculators take care of that.
