In both the U.S. and Canada, amateur radio operators serve an important role in providing emergency radio communications during war, disaster, terrorist attack, or whatever other emergency. So amateur radio operators take an extremely dim view of unlicensed operators using frequencies allocated to amateur (or sometimes commercial) radio. Many will even hunt down unlicensed transmitters and report them to authorities. Radio Amateurs of Canada says that fines can "run to hundreds of dollars," but in the U.S., fines start at $10,000 and go up dramatically from there.
In the U.S., 446 MHz is used nationwide as a simplex calling frequency, so if you are transmitting on PMR 446 channel 1 at 446.00625 MHz, you almost certainly will be noticed, and you probably will be noticed on any other channel. This frequency is also in the band plan in Canada for the same purpose.
If you can avoid doing so, it's a good idea to not use amateur radio frequencies without being licensed. It's not terribly difficult or expensive to become licensed, so it's an option worth looking into. Even so, in this band in both the U.S. and Canada amateur radio operators are secondary users of the band and must yield to primary users, such as...the U.S. military.
If you are close enough to a PAVE PAWS military radar, your PMR446 transmission also may interfere with it, since it uses the same frequency band. In your proposed travel, the nearest such installation is at the Clear Air Force Station in Denali, Alaska. You do not want to mess with the US Department of Defense's ability to detect intercontinental ballistic missiles.
My recommendation would be to replace the radios with FRS/GMRS radios and to keep the PMR446 radios, in case you ever return to Europe. (Note that GMRS does not require a license in Canada, but it does in the United States.)
Beginning in June 2014, MURS, which has been available in the U.S. for several years, will also become an option in Canada. It has higher transmitter power limits (2 watts) and, interestingly, far fewer users, at least in the U.S. When these radios become generally available in Canada, this may make a good alternative to FRS/GMRS if you need longer range or signal quality.
Interestingly, while searching the Internet in relation to this question, I learned that some radio baseband processors can handle FRS, GMRS, MURS and PMR446 on the same chip, so in principle a switchable radio could be built that would operate on FRS/GMRS or MURS in North America and PMR446 in Europe, but I was not able to find any such radio on the market. Such radios might appear on the market in the next few years, or I might need to search more thoroughly. It may also be illegal to market such a radio in some countries.
Along the same lines, many mass-market PMR446 radios have a nearly identical version with the same model number which is programmed for FRS/GMRS instead, so if you are happy with your existing radios, you can buy (nearly) identical ones that use FRS/GMRS.
Another option is to purchase a programmable radio, and program in the correct frequencies corresponding to FRS, GMRS, MURS or PMR446, depending on where you will use it. The two main problems with this approach are also legal: Such radios are usually certified as business radios and thus may not be entirely legal to operate unlicensed, and their power output may also be higher than is allowed for unlicensed operation on these frequencies. One popular example of such a radio is the Baofeng UV-5R. In its low power mode it still transmits at 1 watt, higher than the maximum 500 mW allowed for FRS. It's less likely that you will be caught for this, but it is still possible.