Can I put either a TM on my company logo or a ® without registering it?

As Mr. Rosenbloom said, the TM or SM is a statement of claim. “I claim this mark as my trademark, based on my using it.” You need not register after that, although there are benefits if you succeed in registering. Using the ® without registration is fraud although it is not entirely clear what the penalties might be. Certainly if you use the ® before applying t to the USPTO to register, and they find out, they are likely to refuse registration and be upheld by the courts. There is no clear criminal penalty under federal law.

The R in a circle is the Federal registration symbol and is equivalent to saying "Registered, United States Patent and Trademark Office". 15 USC 1111. You are prohibited from using it if the logo is not registered, because that would be false advertising and false marking. It may render an later trademark registration invalid. The Federal Circuit has held that the improper use of a registration notice in connection with an unregistered mark, if done with intent to deceive the purchasing public or others in the trade into believing that the mark is registered, is a ground for denying the registration of an otherwise registrable mark.”Copelands’ Enterprises Inc. v. CNV Inc., 945 F.2d 1563, 20 USPQ2d 1295 (Fed. Cir. 1991). Under TMEP 906 the USPTO will refuse registration if a specimen of use in an application for registration falsely uses the Federal registration symbol in relation to the goods for which registration is sought. On the other hand, the Federal registration symbol is important to use when the mark is registered due to the damages limitation in 15 USC 1111 which states: "a registrant of a mark registered in the Patent and Trademark Office, may give notice that his mark is registered by displaying with the mark the words “Registered in U.S. Patent and Trademark Office” or “Reg. U.S. Pat. & Tm. Off.” or the letter R enclosed within a circle, thus ®; and in any suit for infringement under this chapter by such a registrant failing to give such notice of registration, no profits and no damages shall be recovered under the provisions of this chapter unless the defendant had actual notice of the registration." The TM or SM symbol are equivalent to saying "I claim this a my trademark" or "I claim this as my servicemark", respectively. They can be used whether or not the trademark or servicemark is registered, but are not binding upon anyone. They are generally used when the mark is one for which registration has been applied at the USPTO but for which the registration has not yet been granted. Using TM or SM on a registered mark will, as noted above, may invoke the damages prohibition of 15 USC 111. Sorry for the long-winded answer, but a simple yes or not is not enough. It is more complex than that. As what you lose by failing to register, among them are the benefits of Federal remedies, presumptions of ownership, ability to register with US Customs (CBP-ICE), foreign recognition for priority, and potential "incontestibility", which make failure to register generally inexcusably poor business judgment.